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 [2291 journals] |
- Blocked semifoldovers of two-level orthogonal designs
- Abstract: Abstract
Follow-up experimentation is often necessary to the successful use of fractional factorial designs. When some effects are believed to be significant but cannot be estimated using an initial design, adding another fraction is often recommended. As the initial design and its foldover (or semifoldover) are usually conducted at different stages, it may be desirable to include a block factor. In this article, we study the blocking effect of such a factor on foldover and semifoldover designs. We consider two general cases for the initial designs, which can be either unblocked or blocked designs. In both cases, we explore the relationships between semifoldover of a design and its corresponding foldover design. More specifically, we obtain some theoretical results on when a semifoldover design can estimate the same two-factor interactions or main effects as the corresponding foldover. These results can be important for those who want to take advantage of the run size savings of a semifoldover without sacrificing the ability to estimate important effects.
PubDate: 2015-07-01
- Abstract: Abstract
Follow-up experimentation is often necessary to the successful use of fractional factorial designs. When some effects are believed to be significant but cannot be estimated using an initial design, adding another fraction is often recommended. As the initial design and its foldover (or semifoldover) are usually conducted at different stages, it may be desirable to include a block factor. In this article, we study the blocking effect of such a factor on foldover and semifoldover designs. We consider two general cases for the initial designs, which can be either unblocked or blocked designs. In both cases, we explore the relationships between semifoldover of a design and its corresponding foldover design. More specifically, we obtain some theoretical results on when a semifoldover design can estimate the same two-factor interactions or main effects as the corresponding foldover. These results can be important for those who want to take advantage of the run size savings of a semifoldover without sacrificing the ability to estimate important effects.
- Classes of multiple decision functions strongly controlling FWER and FDR
- Abstract: Abstract
Two general classes of multiple decision functions, where each member of the first class strongly controls the family-wise error rate (FWER), while each member of the second class strongly controls the false discovery rate (FDR), are described. These classes offer the possibility that optimal multiple decision functions with respect to a pre-specified Type II error criterion, such as the missed discovery rate (MDR), could be found which control the FWER or FDR Type I error rates. The gain in MDR of the associated FDR-controlling procedure relative to the well-known Benjamini–Hochberg procedure is demonstrated via a modest simulation study with gamma-distributed component data. Such multiple decision functions may have the potential of being utilized in multiple testing, specifically in the analysis of high-dimensional data sets.
PubDate: 2015-07-01
- Abstract: Abstract
Two general classes of multiple decision functions, where each member of the first class strongly controls the family-wise error rate (FWER), while each member of the second class strongly controls the false discovery rate (FDR), are described. These classes offer the possibility that optimal multiple decision functions with respect to a pre-specified Type II error criterion, such as the missed discovery rate (MDR), could be found which control the FWER or FDR Type I error rates. The gain in MDR of the associated FDR-controlling procedure relative to the well-known Benjamini–Hochberg procedure is demonstrated via a modest simulation study with gamma-distributed component data. Such multiple decision functions may have the potential of being utilized in multiple testing, specifically in the analysis of high-dimensional data sets.
- Robust tests for the equality of two normal means based on the density
power divergence- Abstract: Abstract
Statistical techniques are used in all branches of science to determine the feasibility of quantitative hypotheses. One of the most basic applications of statistical techniques in comparative analysis is the test of equality of two population means, generally performed under the assumption of normality. In medical studies, for example, we often need to compare the effects of two different drugs, treatments or preconditions on the resulting outcome. The most commonly used test in this connection is the two sample
\(t\)
test for the equality of means, performed under the assumption of equality of variances. It is a very useful tool, which is widely used by practitioners of all disciplines and has many optimality properties under the model. However, the test has one major drawback; it is highly sensitive to deviations from the ideal conditions, and may perform miserably under model misspecification and the presence of outliers. In this paper we present a robust test for the two sample hypothesis based on the density power divergence measure (Basu et al. in Biometrika 85(3):549–559, 1998), and show that it can be a great alternative to the ordinary two sample
\(t\)
test. The asymptotic properties of the proposed tests are rigorously established in the paper, and their performances are explored through simulations and real data analysis.
PubDate: 2015-07-01
- Abstract: Abstract
Statistical techniques are used in all branches of science to determine the feasibility of quantitative hypotheses. One of the most basic applications of statistical techniques in comparative analysis is the test of equality of two population means, generally performed under the assumption of normality. In medical studies, for example, we often need to compare the effects of two different drugs, treatments or preconditions on the resulting outcome. The most commonly used test in this connection is the two sample
\(t\)
test for the equality of means, performed under the assumption of equality of variances. It is a very useful tool, which is widely used by practitioners of all disciplines and has many optimality properties under the model. However, the test has one major drawback; it is highly sensitive to deviations from the ideal conditions, and may perform miserably under model misspecification and the presence of outliers. In this paper we present a robust test for the two sample hypothesis based on the density power divergence measure (Basu et al. in Biometrika 85(3):549–559, 1998), and show that it can be a great alternative to the ordinary two sample
\(t\)
test. The asymptotic properties of the proposed tests are rigorously established in the paper, and their performances are explored through simulations and real data analysis.
- Bahadur representations for bootstrap quantiles
- Abstract: Abstract
A bootstrap sample may contain more than one replica of original data points. To extend the classical Bahadur type representations for the sample quantiles in the independent identical distributed case to bootstrap sample quantiles therefore is not a trivial task. This manuscript fulfils the task and establishes the asymptotic theory of bootstrap sample quantiles.
PubDate: 2015-07-01
- Abstract: Abstract
A bootstrap sample may contain more than one replica of original data points. To extend the classical Bahadur type representations for the sample quantiles in the independent identical distributed case to bootstrap sample quantiles therefore is not a trivial task. This manuscript fulfils the task and establishes the asymptotic theory of bootstrap sample quantiles.
- On estimating the tail index and the spectral measure of multivariate
$$\alpha $$ α -stable distributions- Abstract: Abstract
We propose estimators for the tail index and the spectral measure of multivariate
\(\alpha \)
-stable distributions and derive their asymptotic properties. Simulation studies reveal the appropriateness of the estimators. Applications to financial data are also considered.
PubDate: 2015-07-01
- Abstract: Abstract
We propose estimators for the tail index and the spectral measure of multivariate
\(\alpha \)
-stable distributions and derive their asymptotic properties. Simulation studies reveal the appropriateness of the estimators. Applications to financial data are also considered.
- Estimating covariate functions associated to multivariate risks: a level
set approach- Abstract: Abstract
The aim of this paper is to study the behavior of a covariate function in a multivariate risks scenario. The first part of this paper deals with the problem of estimating the
\(c\)
-upper level sets
\({L(c)= \{F(x) \ge c \}}\)
, with
\(c \in (0,1)\)
, of an unknown distribution function
\(F\)
on
\(\mathbb {R}^d_+\)
. A plug-in approach is followed. We state consistency results with respect to the volume of the symmetric difference. In the second part, we obtain the
\(L_p\)
-consistency, with a convergence rate, for the regression function estimate on these level sets
\(L(c)\)
. We also consider a new multivariate risk measure: the Covariate-Conditional-Tail-Expectation. We provide a consistent estimator for this measure with a convergence rate. We propose a consistent estimate when the regression cannot be estimated on the whole data set. Then, we investigate the effects of scaling data on our consistency results. All these results are proven in a non-compact setting. A complete simulation study is detailed and a comparison with parametric and semi-parametric approaches is provided. Finally, a real environmental application of our risk measure is provided.
PubDate: 2015-07-01
- Abstract: Abstract
The aim of this paper is to study the behavior of a covariate function in a multivariate risks scenario. The first part of this paper deals with the problem of estimating the
\(c\)
-upper level sets
\({L(c)= \{F(x) \ge c \}}\)
, with
\(c \in (0,1)\)
, of an unknown distribution function
\(F\)
on
\(\mathbb {R}^d_+\)
. A plug-in approach is followed. We state consistency results with respect to the volume of the symmetric difference. In the second part, we obtain the
\(L_p\)
-consistency, with a convergence rate, for the regression function estimate on these level sets
\(L(c)\)
. We also consider a new multivariate risk measure: the Covariate-Conditional-Tail-Expectation. We provide a consistent estimator for this measure with a convergence rate. We propose a consistent estimate when the regression cannot be estimated on the whole data set. Then, we investigate the effects of scaling data on our consistency results. All these results are proven in a non-compact setting. A complete simulation study is detailed and a comparison with parametric and semi-parametric approaches is provided. Finally, a real environmental application of our risk measure is provided.
- Distribution function estimation via Bernstein polynomial of random degree
- Abstract: Abstract
The problem of distribution function (df) estimation arises naturally in many contexts. The empirical and the kernel df estimators are well known. There is another df estimator based on a Bernstein polynomial of degree m. For a Bernstein df estimator,
plays the same role as the bandwidth in a kernel estimator. The asymptotic properties of the Bernstein estimator has been studied so far assuming m is non random, chosen subjectively. We propose algorithms for data driven choice of m. Such an m is a function of the data, i.e. random. We obtain the convergence rates of a Bernstein df estimator, using a random m, for i.i.d., strongly mixing and a broad class of linear processes. The estimator is shown to be consistent for any stationary, ergodic process satisfying some conditions. Using simulations and analysis of real data the finite sample performance of the different df estimators are compared.
PubDate: 2015-06-26
- Abstract: Abstract
The problem of distribution function (df) estimation arises naturally in many contexts. The empirical and the kernel df estimators are well known. There is another df estimator based on a Bernstein polynomial of degree m. For a Bernstein df estimator,
plays the same role as the bandwidth in a kernel estimator. The asymptotic properties of the Bernstein estimator has been studied so far assuming m is non random, chosen subjectively. We propose algorithms for data driven choice of m. Such an m is a function of the data, i.e. random. We obtain the convergence rates of a Bernstein df estimator, using a random m, for i.i.d., strongly mixing and a broad class of linear processes. The estimator is shown to be consistent for any stationary, ergodic process satisfying some conditions. Using simulations and analysis of real data the finite sample performance of the different df estimators are compared.
- A note on the strong consistency of M-estimates in linear models
- Abstract: Abstract
We improve a known result on the strong consistency of M-estimates of the regression parameters in a linear model for independent and identically distributed random errors under some mild conditions.
PubDate: 2015-06-23
- Abstract: Abstract
We improve a known result on the strong consistency of M-estimates of the regression parameters in a linear model for independent and identically distributed random errors under some mild conditions.
- Information bounds for nonparametric estimators of L -functionals and
survival functionals under censored data- Abstract: 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: 2015-06-06
- Abstract: 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.
- Connection between uniform and serial correlation structure in the growth
curve model- Abstract: 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: 2015-06-04
- Abstract: 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: 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: 2015-06-02
- Abstract: 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: 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: 2015-06-02
- Abstract: 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.
- Erratum to: Estimating covariate functions associated to multivariate
risks: a level set approach- PubDate: 2015-05-22
- PubDate: 2015-05-22
- Representations of the inactivity time for coherent systems with
heterogeneous components and some ordered properties- Abstract: 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: 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: 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: 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: 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: 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.
- Limit results for concomitants of order statistics
- Abstract: 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: 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: 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: 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.
- A note on relationships between some univariate stochastic orders and the
corresponding joint stochastic orders- Abstract: 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: 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: 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: 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.