Metrika [SJR: 0.943] [H-I: 25] [5 followers] Follow Hybrid journal (It can contain Open Access articles) ISSN (Print) 1435-926X - ISSN (Online) 0026-1335 Published by Springer-Verlag [2302 journals] |
- On the stochastic and dependence properties of the three-state systems
- Abstract: Abstract
Suppose that a system has three states up, partial performance and down. We assume that for a random time
\(T_1\)
the system is in state up, then it moves to state partial performance for time
\(T_2\)
and then the system fails and goes to state down. We also denote the lifetime of the system by
\(T\)
, which is clearly
\(T=T_1+T_2\)
. In this paper, several stochastic comparisons are made between
\(T\)
,
\(T_1\)
and
\(T_2\)
and their reliability properties are also investigated. We prove, among other results, that different concepts of dependence between the elements of the signatures (which are structural properties of the system) are preserved by the lifetimes of the states of the system (which are aging properties of the system). Various illustrative examples are provided.
PubDate: 2015-04-01
- Abstract: Abstract
Suppose that a system has three states up, partial performance and down. We assume that for a random time
\(T_1\)
the system is in state up, then it moves to state partial performance for time
\(T_2\)
and then the system fails and goes to state down. We also denote the lifetime of the system by
\(T\)
, which is clearly
\(T=T_1+T_2\)
. In this paper, several stochastic comparisons are made between
\(T\)
,
\(T_1\)
and
\(T_2\)
and their reliability properties are also investigated. We prove, among other results, that different concepts of dependence between the elements of the signatures (which are structural properties of the system) are preserved by the lifetimes of the states of the system (which are aging properties of the system). Various illustrative examples are provided.
- Circular block bootstrap for coefficients of autocovariance function of
almost periodically correlated time series- Abstract: Abstract
In the paper the consistency of the circular block bootstrap for the coefficients of the autocovariance function of almost periodically correlated time series is proved. The pointwise and the simultaneous bootstrap equal-tailed confidence intervals for these coefficients are constructed. Application of the results to detect the second-order significant frequencies is provided. The simulation and real data examples are also presented.
PubDate: 2015-04-01
- Abstract: Abstract
In the paper the consistency of the circular block bootstrap for the coefficients of the autocovariance function of almost periodically correlated time series is proved. The pointwise and the simultaneous bootstrap equal-tailed confidence intervals for these coefficients are constructed. Application of the results to detect the second-order significant frequencies is provided. The simulation and real data examples are also presented.
- Asymptotic properties of the number of near minimum-concomitant
observations in the case of progressive type-II censoring- Abstract: 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: 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: 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: 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: 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: 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: 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: 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.
- A new derivation of BLUPs under random-effects model
- Abstract: Abstract
This paper considers predictions of vectors of parameters under a general linear model
\(\mathbf{y}= \mathbf{X}{\pmb {\beta }}+ {\pmb {\varepsilon }}\)
with the random coefficients
\({\pmb {\beta }}\)
satisfying
\({\pmb {\beta }}=\mathbf{A}{\pmb {\alpha }}+ {\pmb {\gamma }}\)
. It utilizes a standard method of solving constrained quadratic matrix-valued function optimization problem in the Löwner partial ordering, and obtains the best linear unbiased predictor (BLUP) of given vector
\(\mathbf{F}{\pmb {\alpha }}+ \mathbf{G}\varvec{\gamma } + \mathbf{H}{\pmb {\varepsilon }}\)
of the unknown parameters in the model. Some special cases of the BLUPs are also presented. In particular, a general decomposition equality
\(\mathbf{y}= \mathrm{BLUE}(\mathbf{X}\mathbf{A}{\pmb {\alpha }}) + \mathrm{BLUP}(\mathbf{X}{\pmb {\gamma }}) + \mathrm{BLUP}({\pmb {\varepsilon }})\)
is proved under the random-effects model. A further problem on BLUPs of new observations under the random-effects model is also addressed.
PubDate: 2015-02-26
- Abstract: Abstract
This paper considers predictions of vectors of parameters under a general linear model
\(\mathbf{y}= \mathbf{X}{\pmb {\beta }}+ {\pmb {\varepsilon }}\)
with the random coefficients
\({\pmb {\beta }}\)
satisfying
\({\pmb {\beta }}=\mathbf{A}{\pmb {\alpha }}+ {\pmb {\gamma }}\)
. It utilizes a standard method of solving constrained quadratic matrix-valued function optimization problem in the Löwner partial ordering, and obtains the best linear unbiased predictor (BLUP) of given vector
\(\mathbf{F}{\pmb {\alpha }}+ \mathbf{G}\varvec{\gamma } + \mathbf{H}{\pmb {\varepsilon }}\)
of the unknown parameters in the model. Some special cases of the BLUPs are also presented. In particular, a general decomposition equality
\(\mathbf{y}= \mathrm{BLUE}(\mathbf{X}\mathbf{A}{\pmb {\alpha }}) + \mathrm{BLUP}(\mathbf{X}{\pmb {\gamma }}) + \mathrm{BLUP}({\pmb {\varepsilon }})\)
is proved under the random-effects model. A further problem on BLUPs of new observations under the random-effects model is also addressed.
- Generalized variable resolution designs
- Abstract: Abstract
In this paper, the concept of generalized variable resolution is proposed for designs with nonnegligible interactions between groups. The conditions for the existence of generalized variable resolution designs are discussed. Connections between different generalized variable resolution designs and compromise plans, clear compromise plans and designs containing partially clear two-factor interactions are explored. A general construction method for the proposed designs is also discussed.
PubDate: 2015-02-13
- Abstract: Abstract
In this paper, the concept of generalized variable resolution is proposed for designs with nonnegligible interactions between groups. The conditions for the existence of generalized variable resolution designs are discussed. Connections between different generalized variable resolution designs and compromise plans, clear compromise plans and designs containing partially clear two-factor interactions are explored. A general construction method for the proposed designs is also discussed.
- A Poisson INAR(1) model with serially dependent innovations
- Abstract: Abstract
Motivated by a certain type of infinite-patch metapopulation model, we propose an extension to the popular Poisson INAR(1) model, where the innovations are assumed to be serially dependent in such a way that their mean is increased if the current population is large. We shall recognize that this new model forms a bridge between the Poisson INAR(1) model and the INARCH(1) model. We analyze the stochastic properties of the observations and innovations from an extended Poisson INAR(1) process, and we consider the problem of model identification and parameter estimation. A real-data example about iceberg counts shows how to benefit from the new model.
PubDate: 2015-02-12
- Abstract: Abstract
Motivated by a certain type of infinite-patch metapopulation model, we propose an extension to the popular Poisson INAR(1) model, where the innovations are assumed to be serially dependent in such a way that their mean is increased if the current population is large. We shall recognize that this new model forms a bridge between the Poisson INAR(1) model and the INARCH(1) model. We analyze the stochastic properties of the observations and innovations from an extended Poisson INAR(1) process, and we consider the problem of model identification and parameter estimation. A real-data example about iceberg counts shows how to benefit from the new model.
- Tests in variance components models under skew-normal settings
- Abstract: Abstract
The hypothesis testing problems of unknown parameters for the variance components model with skew-normal random errors are discussed. Several properties of the model, such as the density function, moment generating function, and independence conditions, are obtained. A new version of Cochran’s theorem is given, which is used to establish exact tests for fixed effects and variance components of the model. For illustration, our main results are applied to two examples and a real data problem. Finally, some simulation results on the type I error probability and power of the proposed test are reported. And the simulation results indicate that the proposed test provides satisfactory performance on the type I error probability and power.
PubDate: 2015-02-07
- Abstract: Abstract
The hypothesis testing problems of unknown parameters for the variance components model with skew-normal random errors are discussed. Several properties of the model, such as the density function, moment generating function, and independence conditions, are obtained. A new version of Cochran’s theorem is given, which is used to establish exact tests for fixed effects and variance components of the model. For illustration, our main results are applied to two examples and a real data problem. Finally, some simulation results on the type I error probability and power of the proposed test are reported. And the simulation results indicate that the proposed test provides satisfactory performance on the type I error probability and power.
- Admissibility in non-regular family under squared-log error loss
- Abstract: Abstract
Consider an estimation problem under the squared-log error loss function in a one-parameter non-regular distribution when the endpoint of the support depends on an unknown parameter. The purpose of this paper is to give sufficient conditions for a generalized Bayes estimator of a parametric function to be admissible. Some examples are given.
PubDate: 2015-02-01
- Abstract: Abstract
Consider an estimation problem under the squared-log error loss function in a one-parameter non-regular distribution when the endpoint of the support depends on an unknown parameter. The purpose of this paper is to give sufficient conditions for a generalized Bayes estimator of a parametric function to be admissible. Some examples are given.
- A characterization of the innovations of first order autoregressive models
- Abstract: Abstract
Suppose that
\(Y_t\)
follows a simple AR(1) model, that is, it can be expressed as
\(Y_t= \alpha Y_{t-1} + W_t\)
, where
\(W_t\)
is a white noise with mean equal to
\(\mu \)
and variance
\(\sigma ^2\)
. There are many examples in practice where these assumptions hold very well. Consider
\(X_t = e^{Y_t}\)
. We shall show that the autocorrelation function of
\(X_t\)
characterizes the distribution of
\(W_t\)
.
PubDate: 2015-02-01
- Abstract: Abstract
Suppose that
\(Y_t\)
follows a simple AR(1) model, that is, it can be expressed as
\(Y_t= \alpha Y_{t-1} + W_t\)
, where
\(W_t\)
is a white noise with mean equal to
\(\mu \)
and variance
\(\sigma ^2\)
. There are many examples in practice where these assumptions hold very well. Consider
\(X_t = e^{Y_t}\)
. We shall show that the autocorrelation function of
\(X_t\)
characterizes the distribution of
\(W_t\)
.
- Optimal bounds on expectations of order statistics and spacings from
nonparametric families of distributions generated by convex transform
order- Abstract: Abstract
Assume that
\(X_1,\ldots , X_n\)
are i.i.d. random variables with a common distribution function
\(F\)
which precedes a fixed distribution function
\(W\)
in the convex transform order. In particular, if
\(W\)
is either uniform or exponential distribution function, then
\(F\)
has increasing density and failure rate, respectively. We present sharp upper bounds on the expectations of single order statistics and spacings based on
\(X_1,\ldots , X_n\)
, expressed in terms of the population mean and standard deviation, for the family of all parent distributions preceding
\(W\)
in the convex transform order. We also characterize the distributions which attain the bounds, and specify the general results for the distributions with increasing density function.
PubDate: 2015-02-01
- Abstract: Abstract
Assume that
\(X_1,\ldots , X_n\)
are i.i.d. random variables with a common distribution function
\(F\)
which precedes a fixed distribution function
\(W\)
in the convex transform order. In particular, if
\(W\)
is either uniform or exponential distribution function, then
\(F\)
has increasing density and failure rate, respectively. We present sharp upper bounds on the expectations of single order statistics and spacings based on
\(X_1,\ldots , X_n\)
, expressed in terms of the population mean and standard deviation, for the family of all parent distributions preceding
\(W\)
in the convex transform order. We also characterize the distributions which attain the bounds, and specify the general results for the distributions with increasing density function.
- A robust two-stage procedure in Bayes sequential estimation of a
particular exponential family- Abstract: Abstract
The problem of Bayes sequential estimation of the unknown parameter in a particular exponential family of distributions is considered under linear exponential loss function for estimation error and a fixed cost for each observation. Instead of fully sequential sampling, a two-stage sampling technique is introduced to solve the problem in this paper. The proposed two-stage procedure is robust in the sense that it does not depend on the parameters of the conjugate prior. It is shown that the two-stage procedure is asymptotically pointwise optimal and asymptotically optimal for a large class of the conjugate priors. A simulation study is conducted to compare the performances of the two-stage procedure and the purely sequential procedure.
PubDate: 2015-02-01
- Abstract: Abstract
The problem of Bayes sequential estimation of the unknown parameter in a particular exponential family of distributions is considered under linear exponential loss function for estimation error and a fixed cost for each observation. Instead of fully sequential sampling, a two-stage sampling technique is introduced to solve the problem in this paper. The proposed two-stage procedure is robust in the sense that it does not depend on the parameters of the conjugate prior. It is shown that the two-stage procedure is asymptotically pointwise optimal and asymptotically optimal for a large class of the conjugate priors. A simulation study is conducted to compare the performances of the two-stage procedure and the purely sequential procedure.
- Minimum distance lack-of-fit tests under long memory errors
- Abstract: Abstract
This paper discusses some tests of lack-of-fit of a parametric regression model when errors form a long memory moving average process with the long memory parameter
\(0<d<1/2\)
, and when design is non-random and uniform on
\([0,1]\)
. These tests are based on certain minimized distances between a nonparametric regression function estimator and the parametric model being fitted. The paper investigates the asymptotic null distribution of the proposed test statistics and of the corresponding minimum distance estimators under minimal conditions on the model being fitted. The limiting distribution of these statistics are Gaussian for
\(0<d<1/4\)
and non-Gaussian for
\(1/4<d<1/2\)
. We also discuss the consistency of these tests against a fixed alternative. A simulation study is included to assess the finite sample behavior of the proposed test.
PubDate: 2015-02-01
- Abstract: Abstract
This paper discusses some tests of lack-of-fit of a parametric regression model when errors form a long memory moving average process with the long memory parameter
\(0<d<1/2\)
, and when design is non-random and uniform on
\([0,1]\)
. These tests are based on certain minimized distances between a nonparametric regression function estimator and the parametric model being fitted. The paper investigates the asymptotic null distribution of the proposed test statistics and of the corresponding minimum distance estimators under minimal conditions on the model being fitted. The limiting distribution of these statistics are Gaussian for
\(0<d<1/4\)
and non-Gaussian for
\(1/4<d<1/2\)
. We also discuss the consistency of these tests against a fixed alternative. A simulation study is included to assess the finite sample behavior of the proposed test.
- Linearity of regression for overlapping order statistics
- Abstract: Abstract
We consider a problem of characterization of continuous distributions for which linearity of regression of overlapping order statistics,
\(\mathbb {E}(X_{i:m} X_{j:n})=aX_{j:n}+b\)
,
\(m\le n\)
, holds. Due to a new representation of conditional expectation
\(\mathbb {E}(X_{i:m} X_{j:n})\)
in terms of conditional expectations
\(\mathbb {E}(X_{l:n} X_{j:n})\)
,
\(l=i,\ldots ,n-m+i\)
, we are able to use the already known approach based on the Rao-Shanbhag version of the Cauchy integrated functional equation. However this is possible only if
\(j\le i\)
or
\(j\ge n-m+i\)
. In the remaining cases the problem essentially is still open.
PubDate: 2015-02-01
- Abstract: Abstract
We consider a problem of characterization of continuous distributions for which linearity of regression of overlapping order statistics,
\(\mathbb {E}(X_{i:m} X_{j:n})=aX_{j:n}+b\)
,
\(m\le n\)
, holds. Due to a new representation of conditional expectation
\(\mathbb {E}(X_{i:m} X_{j:n})\)
in terms of conditional expectations
\(\mathbb {E}(X_{l:n} X_{j:n})\)
,
\(l=i,\ldots ,n-m+i\)
, we are able to use the already known approach based on the Rao-Shanbhag version of the Cauchy integrated functional equation. However this is possible only if
\(j\le i\)
or
\(j\ge n-m+i\)
. In the remaining cases the problem essentially is still open.
- Optimal crossover designs in a model with self and mixed carryover effects
with correlated errors- Abstract: Abstract
We determine optimal crossover designs for the estimation of direct treatment effects in a model with mixed and self carryover effects. The model also assumes that the errors within each experimental unit are correlated following a stationary first-order autoregressive process. The paper considers situations where the number of periods for each experimental unit is at least four and the number of treatments is greater or equal to the number of periods.
PubDate: 2015-02-01
- Abstract: Abstract
We determine optimal crossover designs for the estimation of direct treatment effects in a model with mixed and self carryover effects. The model also assumes that the errors within each experimental unit are correlated following a stationary first-order autoregressive process. The paper considers situations where the number of periods for each experimental unit is at least four and the number of treatments is greater or equal to the number of periods.
- Inference for the bivariate Birnbaum–Saunders lifetime regression
model and associated inference- Abstract: Abstract
In this paper, we discuss a regression model based on the bivariate Birnbaum–Saunders distribution. We derive the maximum likelihood estimates of the model parameters and then develop associated inference. Next, we briefly describe likelihood-ratio tests for some hypotheses of interest as well as some interval estimation methods. Monte Carlo simulations are then carried out to examine the performance of the estimators as well as the interval estimation methods. Finally, a numerical data analysis is performed for illustrating all the inferential methods developed here.
PubDate: 2015-01-30
- Abstract: Abstract
In this paper, we discuss a regression model based on the bivariate Birnbaum–Saunders distribution. We derive the maximum likelihood estimates of the model parameters and then develop associated inference. Next, we briefly describe likelihood-ratio tests for some hypotheses of interest as well as some interval estimation methods. Monte Carlo simulations are then carried out to examine the performance of the estimators as well as the interval estimation methods. Finally, a numerical data analysis is performed for illustrating all the inferential methods developed here.
- A dynamic stress–strength model with stochastically decreasing
strength- Abstract: Abstract
We consider a dynamic stress–strength model under external shocks. The strength of the system decreases with time and the failure occurs when the strength finally vanishes. Furthermore, there is another cause of the system failure induced by an external shock process. Each shock is characterized by the corresponding stress. If the magnitude of the stress exceeds the current strength, then the system also fails. We assume that the initial strength of the system and its decreasing drift pattern are random. We derive the survival function of the system and interpret the time-dependent dynamic changes of the random quantities which govern the reliability performance of the system.
PubDate: 2015-01-15
- Abstract: Abstract
We consider a dynamic stress–strength model under external shocks. The strength of the system decreases with time and the failure occurs when the strength finally vanishes. Furthermore, there is another cause of the system failure induced by an external shock process. Each shock is characterized by the corresponding stress. If the magnitude of the stress exceeds the current strength, then the system also fails. We assume that the initial strength of the system and its decreasing drift pattern are random. We derive the survival function of the system and interpret the time-dependent dynamic changes of the random quantities which govern the reliability performance of the system.