Metrika [SJR: 0.943] [H-I: 25] [3 followers] Follow Hybrid journal (It can contain Open Access articles) ISSN (Print) 1435-926X - ISSN (Online) 0026-1335 Published by Springer-Verlag [2302 journals] |
- Representations of the inactivity time for coherent systems with
heterogeneous components and some ordered properties- Abstract: In this paper, we present several useful mixture representations for the reliability function of the inactivity time of systems with heterogeneous components based on order statistics, signatures and mean reliability functions. Some stochastic comparisons of inactivity times between two systems are discussed. These results form nice extensions of some existing results for the case when the components are independent and identically distributed.
PubDate: 2015-05-16
- Abstract: In this paper, we present several useful mixture representations for the reliability function of the inactivity time of systems with heterogeneous components based on order statistics, signatures and mean reliability functions. Some stochastic comparisons of inactivity times between two systems are discussed. These results form nice extensions of some existing results for the case when the components are independent and identically distributed.
- Exponential probability inequality for $$m$$ m -END random variables and
its applications- Abstract: The concept of
\(m\)
-extended negatively dependent (
\(m\)
-END, in short) random variables is introduced and the Kolmogorov exponential inequality for
\(m\)
-END random variables is established. As applications of the Kolmogorov exponential inequality, we further investigate the complete convergence for arrays of rowwise
\(m\)
-END random variables and the complete consistency for the estimator of nonparametric regression models based on
\(m\)
-END errors. Our results generalize and improve some known ones for independent random variables and dependent random variables.
PubDate: 2015-05-14
- Abstract: The concept of
\(m\)
-extended negatively dependent (
\(m\)
-END, in short) random variables is introduced and the Kolmogorov exponential inequality for
\(m\)
-END random variables is established. As applications of the Kolmogorov exponential inequality, we further investigate the complete convergence for arrays of rowwise
\(m\)
-END random variables and the complete consistency for the estimator of nonparametric regression models based on
\(m\)
-END errors. Our results generalize and improve some known ones for independent random variables and dependent random variables.
- Estimating the shape parameter of a Pareto distribution under restrictions
- Abstract: In this paper estimation of the shape parameter of a Pareto distribution is considered under the a priori assumption that it is bounded below by a known constant. The loss function is scale invariant squared error. A class of minimax estimators is presented when the scale parameter of the distribution is known. In consequence, it has been shown that the generalized Bayes estimator with respect to the uniform prior on the truncated parameter space dominates the minimum risk equivariant estimator. By making use of a sequence of proper priors, we also show that this estimator is admissible for estimating the lower bounded shape parameter. A class of truncated linear estimators is studied as well. Some complete class results and a class of minimax estimators for the case of an unknown scale parameter are obtained. The corresponding generalized Bayes estimator is shown to be minimax in this case as well.
PubDate: 2015-05-08
- Abstract: In this paper estimation of the shape parameter of a Pareto distribution is considered under the a priori assumption that it is bounded below by a known constant. The loss function is scale invariant squared error. A class of minimax estimators is presented when the scale parameter of the distribution is known. In consequence, it has been shown that the generalized Bayes estimator with respect to the uniform prior on the truncated parameter space dominates the minimum risk equivariant estimator. By making use of a sequence of proper priors, we also show that this estimator is admissible for estimating the lower bounded shape parameter. A class of truncated linear estimators is studied as well. Some complete class results and a class of minimax estimators for the case of an unknown scale parameter are obtained. The corresponding generalized Bayes estimator is shown to be minimax in this case as well.
- Generalized measures of information for truncated random variables
- Abstract: In the present work we focus on the generalization of two types of measures of information namely divergence-type and entropy-type. Kullback–Leibler discrimination measure and Shannon entropy have been considered in this context for truncated random variables. We propose a generalized discrimination measure between two residual and past lifetime distributions along a similar line of Varma’s entropy. Some properties of this measure are studied and a characterization of the proportional (reversed) hazards model is given. Furthermore, Shannon entropy is generalized on the basis of Varma’s entropy for past lifetime distribution. These results generalize and enhance the related existing results that are developed based on Kullback–Leibler information and Shannon entropy.
PubDate: 2015-05-01
- Abstract: In the present work we focus on the generalization of two types of measures of information namely divergence-type and entropy-type. Kullback–Leibler discrimination measure and Shannon entropy have been considered in this context for truncated random variables. We propose a generalized discrimination measure between two residual and past lifetime distributions along a similar line of Varma’s entropy. Some properties of this measure are studied and a characterization of the proportional (reversed) hazards model is given. Furthermore, Shannon entropy is generalized on the basis of Varma’s entropy for past lifetime distribution. These results generalize and enhance the related existing results that are developed based on Kullback–Leibler information and Shannon entropy.
- Robust minimax Stein estimation under invariant data-based loss for
spherically and elliptically symmetric distributions- Abstract: From an observable
\((X,U)\)
in
\(\mathbb R^p \times \mathbb R^k\)
, we consider estimation of an unknown location parameter
\(\theta \in \mathbb R^p\)
under two distributional settings: the density of
\((X,U)\)
is spherically symmetric with an unknown scale parameter
\(\sigma \)
and is ellipically symmetric with an unknown covariance matrix
\(\Sigma \)
. Evaluation of estimators of
\(\theta \)
is made under the classical invariant losses
\(\Vert d - \theta \Vert ^2 / \sigma ^2\)
and
\((d - \theta )^t \Sigma ^{-1} (d - \theta )\)
as well as two respective data based losses
\(\Vert d - \theta \Vert ^2 / \Vert U\Vert ^2\)
and
\((d - \theta )^t S^{-1} (d - \theta )\)
where
\(\Vert U\Vert ^2\)
estimates
\(\sigma ^2\)
while
\(S\)
estimates
\(\Sigma \)
. We provide new Stein and Stein–Haff identities that allow analysis of risk for these two new losses, including a new identity that gives rise to unbiased estimates of risk (up to a multiple of
\(1 / \sigma ^2\)
) in the spherical case for a larger class of estimators than in Fourdrinier et al. (J Multivar Anal 85:24–39, 2003). Minimax estimators of Baranchik form illustrate the theory. It is found that the range of shrinkage of these estimators is slightly larger for the data based losses compared to the usual invariant losses. It is also found that
\(X\)
is minimax with finite risk with respect to the data-based losses for many distributions for which its risk is infinite when calculated under the classical invariant losses. In these cases, including the multivariate
\(t\)
and, in particular, the multivariate Cauchy, we find improved shrinkage estimators as well.
PubDate: 2015-05-01
- Abstract: From an observable
\((X,U)\)
in
\(\mathbb R^p \times \mathbb R^k\)
, we consider estimation of an unknown location parameter
\(\theta \in \mathbb R^p\)
under two distributional settings: the density of
\((X,U)\)
is spherically symmetric with an unknown scale parameter
\(\sigma \)
and is ellipically symmetric with an unknown covariance matrix
\(\Sigma \)
. Evaluation of estimators of
\(\theta \)
is made under the classical invariant losses
\(\Vert d - \theta \Vert ^2 / \sigma ^2\)
and
\((d - \theta )^t \Sigma ^{-1} (d - \theta )\)
as well as two respective data based losses
\(\Vert d - \theta \Vert ^2 / \Vert U\Vert ^2\)
and
\((d - \theta )^t S^{-1} (d - \theta )\)
where
\(\Vert U\Vert ^2\)
estimates
\(\sigma ^2\)
while
\(S\)
estimates
\(\Sigma \)
. We provide new Stein and Stein–Haff identities that allow analysis of risk for these two new losses, including a new identity that gives rise to unbiased estimates of risk (up to a multiple of
\(1 / \sigma ^2\)
) in the spherical case for a larger class of estimators than in Fourdrinier et al. (J Multivar Anal 85:24–39, 2003). Minimax estimators of Baranchik form illustrate the theory. It is found that the range of shrinkage of these estimators is slightly larger for the data based losses compared to the usual invariant losses. It is also found that
\(X\)
is minimax with finite risk with respect to the data-based losses for many distributions for which its risk is infinite when calculated under the classical invariant losses. In these cases, including the multivariate
\(t\)
and, in particular, the multivariate Cauchy, we find improved shrinkage estimators as well.
- Limit results for concomitants of order statistics
- Abstract: In this paper, we discuss the concomitants of order statistics. We study asymptotic properties of the concomitants of largest order statistics and we pay special attention to strong limit results. The strong limit results of this work are derived by applying the Borel–Cantelli lemma and some of its recent generalizations. The theoretical results of this paper are illustrated with examples.
PubDate: 2015-05-01
- Abstract: In this paper, we discuss the concomitants of order statistics. We study asymptotic properties of the concomitants of largest order statistics and we pay special attention to strong limit results. The strong limit results of this work are derived by applying the Borel–Cantelli lemma and some of its recent generalizations. The theoretical results of this paper are illustrated with examples.
- Construction and selection of the optimal balanced blocked definitive
screening design- Abstract: The definitive screening (DS) design was proposed recently. This new class of three-level designs provides efficient estimates of main effects that are unaliased with any second-order effects. For practical use, we further study the optimal scheme for blocking DS designs. We propose a construction method and utilize the blocked count function to select the optimal balanced blocked definitive screening (BBDS) design in terms of generalized minimum aberration. The proposed BBDS design not only inherits properties of the original DS design but also guarantees that main effects are unconfounded by block effects. Besides that, it has minimum run size and is a saturated design for estimating the mean, all block effects, all main effects, and all quadratic effects.
PubDate: 2015-05-01
- Abstract: The definitive screening (DS) design was proposed recently. This new class of three-level designs provides efficient estimates of main effects that are unaliased with any second-order effects. For practical use, we further study the optimal scheme for blocking DS designs. We propose a construction method and utilize the blocked count function to select the optimal balanced blocked definitive screening (BBDS) design in terms of generalized minimum aberration. The proposed BBDS design not only inherits properties of the original DS design but also guarantees that main effects are unconfounded by block effects. Besides that, it has minimum run size and is a saturated design for estimating the mean, all block effects, all main effects, and all quadratic effects.
- Optimal evaluations for the bias of trimmed means of $$k$$ k th record
values- Abstract: We provide sharp upper and lower mean-variance bounds on the expectations of trimmed means of
\(k\)
th record values from general family of distributions. Also we improve these bounds in the case of non-trimmed means for parent distributions with decreasing density or decreasing failure rate. They can be viewed as bounds on the bias of approximation of expectation of the parent population by mean or trimmed mean of record values. The results are illustrated with numerical examples.
PubDate: 2015-05-01
- Abstract: We provide sharp upper and lower mean-variance bounds on the expectations of trimmed means of
\(k\)
th record values from general family of distributions. Also we improve these bounds in the case of non-trimmed means for parent distributions with decreasing density or decreasing failure rate. They can be viewed as bounds on the bias of approximation of expectation of the parent population by mean or trimmed mean of record values. The results are illustrated with numerical examples.
- A note on relationships between some univariate stochastic orders and the
corresponding joint stochastic orders- Abstract: In order to take into account any possible dependence between alternatives in optimization problems, bivariate characterizations of some well-know univariate stochastic orders have been defined and studied by Shanthikumar and Yao (Adv Appl Probab 23:642–659, 1991). These characterizations gave rise to new stochastic comparisons, commonly called joint stochastic orders, which are equivalent to the original ones under assumption of independence, but are different whenever the variables to be compared are dependent. In this note we provide sufficient conditions on the survival copula describing the dependence among the compared variables such that the standard stochastic orders imply the corresponding joint stochastic orders, and viceversa. Also, simple conditions for joint stochastic orders between the components of random vectors defined through multivariate frailty models are provided.
PubDate: 2015-05-01
- Abstract: In order to take into account any possible dependence between alternatives in optimization problems, bivariate characterizations of some well-know univariate stochastic orders have been defined and studied by Shanthikumar and Yao (Adv Appl Probab 23:642–659, 1991). These characterizations gave rise to new stochastic comparisons, commonly called joint stochastic orders, which are equivalent to the original ones under assumption of independence, but are different whenever the variables to be compared are dependent. In this note we provide sufficient conditions on the survival copula describing the dependence among the compared variables such that the standard stochastic orders imply the corresponding joint stochastic orders, and viceversa. Also, simple conditions for joint stochastic orders between the components of random vectors defined through multivariate frailty models are provided.
- Trimmed and winsorized semiparametric estimator for left-truncated and
right-censored regression models- Abstract: For a linear regression model subject to left-truncation and right-censoring where the truncation and censoring points are known constants (or always observed if random), Karlsson and Laitila (Stat Probab Lett 78:2567–2571, 2008) proposed a semiparametric estimator which deals with left-truncation by trimming and right-censoring by ‘winsorizing’. The estimator was motivated by a zero moment condition where a transformed error term appears with trimmed and winsorized tails. This paper takes the semiparametric estimator further by deriving the asymptotic distribution that was not shown in Karlsson and Laitila (Stat Probab Lett 78:2567–2571, 2008) and discusses its implementation aspects in practice, albeit brief.
PubDate: 2015-05-01
- Abstract: For a linear regression model subject to left-truncation and right-censoring where the truncation and censoring points are known constants (or always observed if random), Karlsson and Laitila (Stat Probab Lett 78:2567–2571, 2008) proposed a semiparametric estimator which deals with left-truncation by trimming and right-censoring by ‘winsorizing’. The estimator was motivated by a zero moment condition where a transformed error term appears with trimmed and winsorized tails. This paper takes the semiparametric estimator further by deriving the asymptotic distribution that was not shown in Karlsson and Laitila (Stat Probab Lett 78:2567–2571, 2008) and discusses its implementation aspects in practice, albeit brief.
- A statistical approach to calibrating the scores of biased reviewers of
scientific papers- Abstract: Peer reviewing is the key ingredient of evaluating the quality of scientific work. Based on the review scores assigned by individual reviewers to papers, program committees of conferences and journal editors decide which papers to accept for publication and which to reject. A similar procedure is part of the selection process of grant applications and, among other fields, in sports. It is well known that the reviewing process suffers from measurement errors due to a lack of agreement among multiple reviewers of the same paper. And if not all papers are reviewed by all reviewers, the naive approach of averaging the scores is biased. Several statistical methods are proposed for aggregating review scores, which all can be realized by standard statistical software. The simplest method uses the well-known fixed-effects two-way classification with identical variances, while a more advanced method assumes different variances. As alternatives a mixed linear model and a generalized linear model are employed. The application of these methods implies an evaluation of the reviewers, which may help to improve reviewing processes. An application example with real conference data shows the potential of these statistical methods.
PubDate: 2015-04-24
- Abstract: Peer reviewing is the key ingredient of evaluating the quality of scientific work. Based on the review scores assigned by individual reviewers to papers, program committees of conferences and journal editors decide which papers to accept for publication and which to reject. A similar procedure is part of the selection process of grant applications and, among other fields, in sports. It is well known that the reviewing process suffers from measurement errors due to a lack of agreement among multiple reviewers of the same paper. And if not all papers are reviewed by all reviewers, the naive approach of averaging the scores is biased. Several statistical methods are proposed for aggregating review scores, which all can be realized by standard statistical software. The simplest method uses the well-known fixed-effects two-way classification with identical variances, while a more advanced method assumes different variances. As alternatives a mixed linear model and a generalized linear model are employed. The application of these methods implies an evaluation of the reviewers, which may help to improve reviewing processes. An application example with real conference data shows the potential of these statistical methods.
- Testing order restrictions in contingency tables
- Abstract: Though several interesting models for contingency tables are defined by a system of inequality constraints on a suitable set of marginal log-linear parameters, the specific features of the corresponding testing problems and the related procedures are not widely well known. After reviewing the most common difficulties which are intrinsic to inequality restricted testing problems, the paper concentrates on the problem of testing a set of equalities against the hypothesis that these are violated in the positive direction and also on testing the corresponding inequalities against the saturated model; we argue that valid procedures should consider these two testing problems simultaneously. By reformulating and adapting procedures appeared in the econometric literature, we propose a likelihood ratio and a multiple comparison procedure which are both based on the joint distribution of two relevant statistics; these statistics are used to divide the sample space into three regions: acceptance of the assumed equality constraints, rejection towards inequalities in the positive direction and rejection towards the unrestricted model. A simulation study indicates that the likelihood ratio based procedure perform substantially better. Our procedures are applied to the analysis of two real data sets to clarify how they work in practice.
PubDate: 2015-04-18
- Abstract: Though several interesting models for contingency tables are defined by a system of inequality constraints on a suitable set of marginal log-linear parameters, the specific features of the corresponding testing problems and the related procedures are not widely well known. After reviewing the most common difficulties which are intrinsic to inequality restricted testing problems, the paper concentrates on the problem of testing a set of equalities against the hypothesis that these are violated in the positive direction and also on testing the corresponding inequalities against the saturated model; we argue that valid procedures should consider these two testing problems simultaneously. By reformulating and adapting procedures appeared in the econometric literature, we propose a likelihood ratio and a multiple comparison procedure which are both based on the joint distribution of two relevant statistics; these statistics are used to divide the sample space into three regions: acceptance of the assumed equality constraints, rejection towards inequalities in the positive direction and rejection towards the unrestricted model. A simulation study indicates that the likelihood ratio based procedure perform substantially better. Our procedures are applied to the analysis of two real data sets to clarify how they work in practice.
- Generalized projection discrepancy and its applications in experimental
designs- Abstract: The objective of this paper is to study the issue of the generalized projection discrepancy along the line of Qin et al. (J Stat Plan Inference 142:1170–1177, 2012) based on generalized discrete discrepancy measure proposed by Chatterjee and Qin (J Stat Plan Inference 141:951–960, 2011). We shall study the projection properties for general asymmetric factorials and provide some analytic connections between minimum generalized projection uniformity and other optimality criteria. A new lower bound on the generalized projection discrepancy for asymmetric factorials is presented here.
PubDate: 2015-04-17
- Abstract: The objective of this paper is to study the issue of the generalized projection discrepancy along the line of Qin et al. (J Stat Plan Inference 142:1170–1177, 2012) based on generalized discrete discrepancy measure proposed by Chatterjee and Qin (J Stat Plan Inference 141:951–960, 2011). We shall study the projection properties for general asymmetric factorials and provide some analytic connections between minimum generalized projection uniformity and other optimality criteria. A new lower bound on the generalized projection discrepancy for asymmetric factorials is presented here.
- A new variable selection approach for varying coefficient models
- Abstract: The varying coefficient models are very important tools to explore the hidden structure between the response variable and its predictors. However, variable selection and identification of varying coefficients of the models are poorly understood. In this paper, we develop a novel method to overcome these difficulties using local polynomial smoothing and the SCAD penalty. Under some regularity conditions, we show that the proposed procedure is consistent in separating the varying coefficients from the constant ones. The resulting estimator can be as efficient as the oracle. Simulation results confirm our theories. Finally, we study the Boston housing data using the proposed method.
PubDate: 2015-04-16
- Abstract: The varying coefficient models are very important tools to explore the hidden structure between the response variable and its predictors. However, variable selection and identification of varying coefficients of the models are poorly understood. In this paper, we develop a novel method to overcome these difficulties using local polynomial smoothing and the SCAD penalty. Under some regularity conditions, we show that the proposed procedure is consistent in separating the varying coefficients from the constant ones. The resulting estimator can be as efficient as the oracle. Simulation results confirm our theories. Finally, we study the Boston housing data using the proposed method.
- Properties of additive frailty model in survival analysis
- Abstract: In this paper, we study a general additive frailty model along with some special cases and examples. The monotonicity of the population hazard is investigated in comparison to the baseline hazard rate. Examples are provided where the unconditional failure rate turns out to be increasing or bathtub shaped even when the baseline hazard is increasing. Association measure, for the additive case, of the correlated life times is studied with several examples.
PubDate: 2015-04-02
- Abstract: In this paper, we study a general additive frailty model along with some special cases and examples. The monotonicity of the population hazard is investigated in comparison to the baseline hazard rate. Examples are provided where the unconditional failure rate turns out to be increasing or bathtub shaped even when the baseline hazard is increasing. Association measure, for the additive case, of the correlated life times is studied with several examples.
- Asymptotic properties of the number of near minimum-concomitant
observations in the case of progressive type-II censoring- Abstract: In this paper, we study the number of near minimum-concomitant observations for Progressively Type-II Censored Order Statistics (PCOS). We first define the concomitants of PCOS and the number of near minimum-concomitant observations. We then investigate distributional and asymptotic properties of these random variables. Finally, we propose simulation techniques for generating the concomitants of PCOS.
PubDate: 2015-04-01
- Abstract: In this paper, we study the number of near minimum-concomitant observations for Progressively Type-II Censored Order Statistics (PCOS). We first define the concomitants of PCOS and the number of near minimum-concomitant observations. We then investigate distributional and asymptotic properties of these random variables. Finally, we propose simulation techniques for generating the concomitants of PCOS.
- Erratum to: On optimal designs for censored data
- PubDate: 2015-04-01
- PubDate: 2015-04-01
- Applications of the Rosenthal-type inequality for negatively superadditive
dependent random variables- Abstract: In this paper, we give some applications of the Rosenthal-type inequality for a sequence of negatively superadditive dependent (NSD) random variables, which includes sequences of negatively associated random variables as a special case. The complete consistency for an estimator of a nonparametric regression model based on NSD errors is investigated. In addition, we extend Feller’s weak law of large numbers for independent and identically distributed random variables to the case of NSD random variables by using the Rosenthal-type inequality.
PubDate: 2015-04-01
- Abstract: In this paper, we give some applications of the Rosenthal-type inequality for a sequence of negatively superadditive dependent (NSD) random variables, which includes sequences of negatively associated random variables as a special case. The complete consistency for an estimator of a nonparametric regression model based on NSD errors is investigated. In addition, we extend Feller’s weak law of large numbers for independent and identically distributed random variables to the case of NSD random variables by using the Rosenthal-type inequality.
- On optimal designs for censored data
- Abstract: In time to event experiments the individuals under study are observed to experience some event of interest. If this event is not observed until the end of the experiment, censoring occurs, which is a common feature in such studies. We consider the proportional hazards model with type I and random censoring and determine locally
\(D\)
- and
\(c\)
-optimal designs for a larger class of nonlinear models with two parameters, where the experimental conditions can be selected from a finite discrete design region, as is often the case in practice. Additionally, we compute
\(D\)
-optimal designs for a three-parameter model on a continuous design region.
PubDate: 2015-04-01
- Abstract: In time to event experiments the individuals under study are observed to experience some event of interest. If this event is not observed until the end of the experiment, censoring occurs, which is a common feature in such studies. We consider the proportional hazards model with type I and random censoring and determine locally
\(D\)
- and
\(c\)
-optimal designs for a larger class of nonlinear models with two parameters, where the experimental conditions can be selected from a finite discrete design region, as is often the case in practice. Additionally, we compute
\(D\)
-optimal designs for a three-parameter model on a continuous design region.
- Inference for types and structured families of commutative orthogonal
block structures- Abstract: Models with commutative orthogonal block structure, COBS, have orthogonal block structure, OBS, and their least square estimators for estimable vectors are, as it will be shown, best linear unbiased estimator, BLUE. Commutative Jordan algebras will be used to study the algebraic structure of the models and to define special types of models for which explicit expressions for the estimation of variance components are obtained. Once normality is assumed, inference using pivot variables is quite straightforward. To illustrate this class of models we will present unbalanced examples before considering families of models. When the models in a family correspond to the treatments of a base design, the family is structured. It will be shown how, under quite general conditions, the action of the factors in the base design on estimable vectors, can be studied.
PubDate: 2015-04-01
- Abstract: Models with commutative orthogonal block structure, COBS, have orthogonal block structure, OBS, and their least square estimators for estimable vectors are, as it will be shown, best linear unbiased estimator, BLUE. Commutative Jordan algebras will be used to study the algebraic structure of the models and to define special types of models for which explicit expressions for the estimation of variance components are obtained. Once normality is assumed, inference using pivot variables is quite straightforward. To illustrate this class of models we will present unbalanced examples before considering families of models. When the models in a family correspond to the treatments of a base design, the family is structured. It will be shown how, under quite general conditions, the action of the factors in the base design on estimable vectors, can be studied.