Metrika [SJR: 0.943] [H-I: 25] [2 followers] Follow Hybrid journal (It can contain Open Access articles) ISSN (Print) 1435-926X - ISSN (Online) 0026-1335 Published by Springer-Verlag [2280 journals] |
- On the records of multivariate random sequences
- Abstract: Two types of records in multivariate sequences are considered in this paper. According to the first definition, a multivariate observation is accepted as a record if it is not dominated in at least one of the coordinates of previous record and the first observation is a record. Some basic straightforward results concerning the distributions of record times and records according to this definition are given. The development of distribution theory for these types of record and also providing examples with available analytical results still involves challenging unsolved problems. Second, we consider records of bivariate sequences according to conditionally N-ordering, introduced in Bairamov (J Multivar Anal 97:797–809, 2006). The joint distributions of record times and distributions of record values are derived. Some examples, with particular underlying distributions demonstrating the availability of obtained formulae are provided.
PubDate: 2016-02-03
- Abstract: Two types of records in multivariate sequences are considered in this paper. According to the first definition, a multivariate observation is accepted as a record if it is not dominated in at least one of the coordinates of previous record and the first observation is a record. Some basic straightforward results concerning the distributions of record times and records according to this definition are given. The development of distribution theory for these types of record and also providing examples with available analytical results still involves challenging unsolved problems. Second, we consider records of bivariate sequences according to conditionally N-ordering, introduced in Bairamov (J Multivar Anal 97:797–809, 2006). The joint distributions of record times and distributions of record values are derived. Some examples, with particular underlying distributions demonstrating the availability of obtained formulae are provided.
- 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: 2016-02-01
- 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.
- Connection between uniform and serial correlation structure in the growth
curve model- Abstract: We introduce a special correlation structure in the growth curve model, which can be viewed as a transition between the serial and the uniform correlation structure. Estimators of unknown variance parameters are derived.
PubDate: 2016-02-01
- Abstract: We introduce a special correlation structure in the growth curve model, which can be viewed as a transition between the serial and the uniform correlation structure. Estimators of unknown variance parameters are derived.
- A goodness-of-fit test for marginal distribution of linear random fields
with long memory- Abstract: This paper addresses the problem of fitting a known distribution function to the marginal distribution of a stationary long memory moving average random field observed on increasing
\(\nu \)
-dimensional “cubic” domains when its mean
\(\mu \)
and scale
\(\sigma \)
are known or unknown. Using two suitable estimators of
\(\mu \)
and a classical estimate of
\(\sigma \)
, a modification of the Kolmogorov–Smirnov statistic is defined based on the residual empirical process and having a Cauchy-type limit distribution, independent of
\(\mu ,\sigma \)
and the long memory parameter d. Based on this result, a simple goodness-of-fit test for the marginal distribution is constructed, which does not require the estimation of d or any other underlying nuisance parameters. The result is new even for the case of time series, i.e., when
\(\nu =1\)
. Findings of a simulation study investigating the finite sample behavior of size and power of the proposed test is also included in this paper.
PubDate: 2016-02-01
- Abstract: This paper addresses the problem of fitting a known distribution function to the marginal distribution of a stationary long memory moving average random field observed on increasing
\(\nu \)
-dimensional “cubic” domains when its mean
\(\mu \)
and scale
\(\sigma \)
are known or unknown. Using two suitable estimators of
\(\mu \)
and a classical estimate of
\(\sigma \)
, a modification of the Kolmogorov–Smirnov statistic is defined based on the residual empirical process and having a Cauchy-type limit distribution, independent of
\(\mu ,\sigma \)
and the long memory parameter d. Based on this result, a simple goodness-of-fit test for the marginal distribution is constructed, which does not require the estimation of d or any other underlying nuisance parameters. The result is new even for the case of time series, i.e., when
\(\nu =1\)
. Findings of a simulation study investigating the finite sample behavior of size and power of the proposed test is also included in this paper.
- Asymptotic efficiency of new exponentiality tests based on a
characterization- Abstract: Two new tests for exponentiality, of integral- and Kolmogorov-type, are proposed. They are based on a recent characterization and formed using appropriate V-statistics. Their asymptotic properties are examined and their local Bahadur efficiencies against some common alternatives are found. A class of locally optimal alternatives for each test is obtained. The powers of these tests, for some small sample sizes, are compared with different exponentiality tests.
PubDate: 2016-02-01
- Abstract: Two new tests for exponentiality, of integral- and Kolmogorov-type, are proposed. They are based on a recent characterization and formed using appropriate V-statistics. Their asymptotic properties are examined and their local Bahadur efficiencies against some common alternatives are found. A class of locally optimal alternatives for each test is obtained. The powers of these tests, for some small sample sizes, are compared with different exponentiality tests.
- Information bounds for nonparametric estimators of L -functionals and
survival functionals under censored data- Abstract: In the present paper we derive lower asymptotic information bounds of Cramér-Rao type for estimators of nonparametric statistical functionals. The results are based on dense differentiability and dense regularity concepts which lead to weak assumptions. As explicit examples L-estimators are treated. In addition a new rapid method for the treatment of survival functionals under randomly right censored data is presented. For instance, for the famous Kaplan-Meier and Nelson-Aalen estimators, our information bound is just the lower bound obtained earlier in the literature.
PubDate: 2016-02-01
- Abstract: In the present paper we derive lower asymptotic information bounds of Cramér-Rao type for estimators of nonparametric statistical functionals. The results are based on dense differentiability and dense regularity concepts which lead to weak assumptions. As explicit examples L-estimators are treated. In addition a new rapid method for the treatment of survival functionals under randomly right censored data is presented. For instance, for the famous Kaplan-Meier and Nelson-Aalen estimators, our information bound is just the lower bound obtained earlier in the literature.
- Erratum to: Testing structural changes in panel data with small fixed
panel size and bootstrap- PubDate: 2016-02-01
- PubDate: 2016-02-01
- 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: 2016-01-01
- 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.
- 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: 2016-01-01
- 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.
- 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: 2016-01-01
- 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.
- 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: 2016-01-01
- 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.
- 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: 2016-01-01
- 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.
- 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: 2016-01-01
- 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.
- 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: 2016-01-01
- 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.
- A new method of kernel-smoothing estimation of the ROC curve
- Abstract: The receiver operating characteristic (ROC) curve is a popular graphical tool for describing the accuracy of a diagnostic test. Based on the idea of estimating the ROC curve as a distribution function, we propose a new kernel smoothing estimator of the ROC curve which is invariant under nondecreasing data transformations. We prove that the estimator has better asymptotic mean squared error properties than some other estimators involving kernel smoothing and we present an easy method of bandwidth selection. By simulation studies, we show that for the limited sample sizes, our proposed estimator is competitive with some other nonparametric estimators of the ROC curve. We also give an example of applying the estimator to a real data set.
PubDate: 2015-12-28
- Abstract: The receiver operating characteristic (ROC) curve is a popular graphical tool for describing the accuracy of a diagnostic test. Based on the idea of estimating the ROC curve as a distribution function, we propose a new kernel smoothing estimator of the ROC curve which is invariant under nondecreasing data transformations. We prove that the estimator has better asymptotic mean squared error properties than some other estimators involving kernel smoothing and we present an easy method of bandwidth selection. By simulation studies, we show that for the limited sample sizes, our proposed estimator is competitive with some other nonparametric estimators of the ROC curve. We also give an example of applying the estimator to a real data set.
- On multi-step MLE-process for Markov sequences
- Abstract: We consider the problem of the construction of the estimator-process of the unknown finite-dimensional parameter in the case of the observations of nonlinear autoregressive process. The estimation is done in two or three steps. First we estimate the unknown parameter by a learning relatively short part of observations and then we use the one-step MLE idea to construct an-estimator process which is asymptotically equivalent to the MLE. To have the learning interval shorter we introduce the two-step procedure which leads to the asymptotically efficient estimator-process too. The presented results are illustrated with the help of two numerical examples.
PubDate: 2015-12-22
- Abstract: We consider the problem of the construction of the estimator-process of the unknown finite-dimensional parameter in the case of the observations of nonlinear autoregressive process. The estimation is done in two or three steps. First we estimate the unknown parameter by a learning relatively short part of observations and then we use the one-step MLE idea to construct an-estimator process which is asymptotically equivalent to the MLE. To have the learning interval shorter we introduce the two-step procedure which leads to the asymptotically efficient estimator-process too. The presented results are illustrated with the help of two numerical examples.
- Evaluations of expectations of order statistics and spacings based on IFR
distributions- Abstract: We consider i.i.d. random variables
\(X_1,\ldots , X_n\)
with a distribution function F preceding the exponential distribution function V in the convex transform order which means that F has an increasing failure rate. We determine sharp upper bounds on the expectations of order statistics and spacings based on
\(X_1,\ldots , X_n\)
, expressed in the population standard deviation units. We also specify the distributions for which all these bounds are attained. Finally, we indicate some reliability applications.
PubDate: 2015-12-15
- Abstract: We consider i.i.d. random variables
\(X_1,\ldots , X_n\)
with a distribution function F preceding the exponential distribution function V in the convex transform order which means that F has an increasing failure rate. We determine sharp upper bounds on the expectations of order statistics and spacings based on
\(X_1,\ldots , X_n\)
, expressed in the population standard deviation units. We also specify the distributions for which all these bounds are attained. Finally, we indicate some reliability applications.
- Robust Bayesian Pitman closeness
- Abstract: In this paper, the robust Bayesian methodology has been developed in the sense of Pitman measure of closeness. To do this, the definition of Pitman posterior closeness, introduced by Ghosh and Sen (Commun Stat Theory Methods 20:3659–3678, 1991) and simultaneous closeness are integrated. First, the
\(\varGamma \)
-minimax problem is developed in the sense of Pitman’s criterion and the basic results and definitions are provided. Then, several results regarding Pitman
\(\varGamma \)
-minimax have been proved. Some examples have been presented to illustrate the application of the findings. Finally, other aspect of robust Bayesian methodology such as: Pitman stable rules and Pitman regret type estimators have been proposed.
PubDate: 2015-12-15
- Abstract: In this paper, the robust Bayesian methodology has been developed in the sense of Pitman measure of closeness. To do this, the definition of Pitman posterior closeness, introduced by Ghosh and Sen (Commun Stat Theory Methods 20:3659–3678, 1991) and simultaneous closeness are integrated. First, the
\(\varGamma \)
-minimax problem is developed in the sense of Pitman’s criterion and the basic results and definitions are provided. Then, several results regarding Pitman
\(\varGamma \)
-minimax have been proved. Some examples have been presented to illustrate the application of the findings. Finally, other aspect of robust Bayesian methodology such as: Pitman stable rules and Pitman regret type estimators have been proposed.
- Variability ordering of multiplicative frailty models
- Abstract: The classical multiplicative frailty model in survival analysis accounts for unobserved heterogeneity between individuals. It is of great importance to identify how the variation of the frailty variable affects that of the overall population. This paper is mainly to present how the dispersive and the excess wealth orders between two frailty variables, translate into the corresponding orders between the resulting overall population variables. For the mean residual life and the mean inactivity time orders, we also obtain relevant analogous results in multiplicative frailty models.
PubDate: 2015-12-12
- Abstract: The classical multiplicative frailty model in survival analysis accounts for unobserved heterogeneity between individuals. It is of great importance to identify how the variation of the frailty variable affects that of the overall population. This paper is mainly to present how the dispersive and the excess wealth orders between two frailty variables, translate into the corresponding orders between the resulting overall population variables. For the mean residual life and the mean inactivity time orders, we also obtain relevant analogous results in multiplicative frailty models.
- Likelihood ratio order of parallel systems with heterogeneous Weibull
components- Abstract: In this paper, we compare the largest order statistics arising from independent heterogeneous Weibull random variables based on the likelihood ratio order. Let
\(X_{1},\ldots ,X_{n}\)
be independent Weibull random variables with
\(X_{i}\)
having shape parameter
\(0<\alpha \le 1\)
and scale parameter
\(\lambda _{i}\)
,
\(i=1,\ldots ,n\)
, and
\(Y_{1},\ldots ,Y_{n}\)
be a random sample of size n from a Weibull distribution with shape parameter
\(0<\alpha \le 1\)
and a common scale parameter
\(\overline{\lambda }=\frac{1}{n}\sum \nolimits _{i=1}^{n}\lambda _{i}\)
, the arithmetic mean of
\(\lambda _{i}^{'}s\)
. Let
\(X_{n:n}\)
and
\(Y_{n:n}\)
denote the corresponding largest order statistics, respectively. We then prove that
\(X_{n:n}\)
is stochastically larger than
\(Y_{n:n}\)
in terms of the likelihood ratio order, and provide numerical examples to illustrate the results established here.
PubDate: 2015-12-11
- Abstract: In this paper, we compare the largest order statistics arising from independent heterogeneous Weibull random variables based on the likelihood ratio order. Let
\(X_{1},\ldots ,X_{n}\)
be independent Weibull random variables with
\(X_{i}\)
having shape parameter
\(0<\alpha \le 1\)
and scale parameter
\(\lambda _{i}\)
,
\(i=1,\ldots ,n\)
, and
\(Y_{1},\ldots ,Y_{n}\)
be a random sample of size n from a Weibull distribution with shape parameter
\(0<\alpha \le 1\)
and a common scale parameter
\(\overline{\lambda }=\frac{1}{n}\sum \nolimits _{i=1}^{n}\lambda _{i}\)
, the arithmetic mean of
\(\lambda _{i}^{'}s\)
. Let
\(X_{n:n}\)
and
\(Y_{n:n}\)
denote the corresponding largest order statistics, respectively. We then prove that
\(X_{n:n}\)
is stochastically larger than
\(Y_{n:n}\)
in terms of the likelihood ratio order, and provide numerical examples to illustrate the results established here.