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 [2276 journals] |
- On runs of ones defined on a q -sequence of binary trials
- Abstract: Abstract
In a sequence of n binary (
\(0{-}1\)
) trials, with probability of ones varying according to a geometric rule, we consider a random variable denoting the number of runs of ones of length at least equal to a fixed threshold k,
\(1\le k\le n\)
. Closed and recursive expressions are obtained for the probability mass function, generating functions and moments of this random variable. Statistical inference problems related to the probability of ones are examined by numerical techniques. Numerics illustrate further the theoretical results.
PubDate: 2015-11-17
- Abstract: Abstract
In a sequence of n binary (
\(0{-}1\)
) trials, with probability of ones varying according to a geometric rule, we consider a random variable denoting the number of runs of ones of length at least equal to a fixed threshold k,
\(1\le k\le n\)
. Closed and recursive expressions are obtained for the probability mass function, generating functions and moments of this random variable. Statistical inference problems related to the probability of ones are examined by numerical techniques. Numerics illustrate further the theoretical results.
- Single change-point detection methods for small lifetime samples
- Abstract: Abstract
In this paper, we address the problem of deciding if either n consecutive independent failure times have the same failure rate or if there exists some
\(k\in \{1,\ldots ,n\}\)
such that the common failure rate of the first k failure times is different from the common failure rate of the last
\(n-k\)
failure times, based on an exponential lifetime distribution. The statistical test we propose is based on the empirical average ratio under the assumption of exponentiality. The proposed test is compared to the one based on the Mann–Whitney statistic for which no parametric assumption on the underlying distribution is necessary. The proposed statistics are free of the unknown underlying distribution under the null hypothesis of homogeneity of the n failure times which enables the determination of critical values of the proposed tests by Monte Carlo methods for small sample sizes.
PubDate: 2015-11-13
- Abstract: Abstract
In this paper, we address the problem of deciding if either n consecutive independent failure times have the same failure rate or if there exists some
\(k\in \{1,\ldots ,n\}\)
such that the common failure rate of the first k failure times is different from the common failure rate of the last
\(n-k\)
failure times, based on an exponential lifetime distribution. The statistical test we propose is based on the empirical average ratio under the assumption of exponentiality. The proposed test is compared to the one based on the Mann–Whitney statistic for which no parametric assumption on the underlying distribution is necessary. The proposed statistics are free of the unknown underlying distribution under the null hypothesis of homogeneity of the n failure times which enables the determination of critical values of the proposed tests by Monte Carlo methods for small sample sizes.
- Stochastic somparisons of order statistics from scaled and interdependent
random variables- Abstract: Abstract
This paper studies order statistics from random variables following the scale model. In the presence of the Archimedean copula or survival copula for the random variables, we obtain the usual stochastic order of the sample extremes and the second smallest order statistic, the dispersive order and the star order of the sample extremes.
PubDate: 2015-11-12
- Abstract: Abstract
This paper studies order statistics from random variables following the scale model. In the presence of the Archimedean copula or survival copula for the random variables, we obtain the usual stochastic order of the sample extremes and the second smallest order statistic, the dispersive order and the star order of the sample extremes.
- A mixture model of size-biased distributions
- Abstract: Abstract
In reliability and survival analysis, to model lifetime data, size-biased distributions are useful. In this paper, a mixture model of size-biased distributions is introduced and studied. Several reliability properties of this model are investigated. In addition, some implications of well-known stochastic orders and aging classes concerning the model are established. To underline the usefulness of the model, some examples of interest in reliability and statistics are given.
PubDate: 2015-11-11
- Abstract: Abstract
In reliability and survival analysis, to model lifetime data, size-biased distributions are useful. In this paper, a mixture model of size-biased distributions is introduced and studied. Several reliability properties of this model are investigated. In addition, some implications of well-known stochastic orders and aging classes concerning the model are established. To underline the usefulness of the model, some examples of interest in reliability and statistics are given.
- Mixed-level designs with resolution III or IV containing clear two-factor
interaction components- Abstract: Abstract
Mixed-level designs are widely used in factorial experiments. Clear effects criterion is one of the important rules for selecting optimal fractional factorial designs. It is highly desirable to know when mixed-level designs with resolution III or IV can have clear two-factor interaction components. This paper considers mixed-level designs with one or two high-level factors and some two-level factors, denoted as
\((2^{r})\times 2^n\)
and
\((2^{r_1})\times (2^{r_2})\times 2^n\)
, respectively, and gives a complete classification of the existence of clear two-factor interaction components in such designs with resolution III or IV. The results reveal the structures of these designs.
PubDate: 2015-11-01
- Abstract: Abstract
Mixed-level designs are widely used in factorial experiments. Clear effects criterion is one of the important rules for selecting optimal fractional factorial designs. It is highly desirable to know when mixed-level designs with resolution III or IV can have clear two-factor interaction components. This paper considers mixed-level designs with one or two high-level factors and some two-level factors, denoted as
\((2^{r})\times 2^n\)
and
\((2^{r_1})\times (2^{r_2})\times 2^n\)
, respectively, and gives a complete classification of the existence of clear two-factor interaction components in such designs with resolution III or IV. The results reveal the structures of these designs.
- Schur properties of convolutions of gamma random variables
- Abstract: Abstract
Sufficient conditions for comparing the convolutions of heterogeneous gamma random variables in terms of the usual stochastic order are established. Such comparisons are characterized by the Schur convexity properties of the cumulative distribution function of the convolutions. Some examples of the practical applications of our results are given.
PubDate: 2015-11-01
- Abstract: Abstract
Sufficient conditions for comparing the convolutions of heterogeneous gamma random variables in terms of the usual stochastic order are established. Such comparisons are characterized by the Schur convexity properties of the cumulative distribution function of the convolutions. Some examples of the practical applications of our results are given.
- Nonlinear wavelet density estimation with data missing at random when
covariates are present- Abstract: Abstract
In this paper, we construct the nonlinear wavelet estimator of a density with data missing at random when covariables are present, and provide an asymptotic expression for the mean integrated squared error (MISE) of the estimator. Unlike for kernel estimators, the MISE expression of the wavelet-based estimator still holds when the density function is piecewise smooth. Also, the asymptotic normality of the estimator is established.
PubDate: 2015-11-01
- Abstract: Abstract
In this paper, we construct the nonlinear wavelet estimator of a density with data missing at random when covariables are present, and provide an asymptotic expression for the mean integrated squared error (MISE) of the estimator. Unlike for kernel estimators, the MISE expression of the wavelet-based estimator still holds when the density function is piecewise smooth. Also, the asymptotic normality of the estimator is established.
- 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: 2015-11-01
- 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.
- Empirical likelihood test in a posteriori change-point nonlinear model
- Abstract: Abstract
In this paper, in order to test whether changes have occurred in a nonlinear parametric regression, we propose a nonparametric method based on the empirical likelihood. Firstly, we test the null hypothesis of no-change against the alternative of one change in the regression parameters. Under null hypothesis, the consistency and the convergence rate of the regression parameter estimators are proved. The asymptotic distribution of the test statistic under the null hypothesis is obtained, which allows to find the asymptotic critical value. On the other hand, we prove that the proposed test statistic has the asymptotic power equal to 1. These theoretical results allows find a simple test statistic, very useful for applications. The epidemic model, a particular model with two change-points under the alternative hypothesis, is also studied. Numerical studies by Monte Carlo simulations show the performance of the proposed test statistic.
PubDate: 2015-11-01
- Abstract: Abstract
In this paper, in order to test whether changes have occurred in a nonlinear parametric regression, we propose a nonparametric method based on the empirical likelihood. Firstly, we test the null hypothesis of no-change against the alternative of one change in the regression parameters. Under null hypothesis, the consistency and the convergence rate of the regression parameter estimators are proved. The asymptotic distribution of the test statistic under the null hypothesis is obtained, which allows to find the asymptotic critical value. On the other hand, we prove that the proposed test statistic has the asymptotic power equal to 1. These theoretical results allows find a simple test statistic, very useful for applications. The epidemic model, a particular model with two change-points under the alternative hypothesis, is also studied. Numerical studies by Monte Carlo simulations show the performance of the proposed test statistic.
- Multivariate stochastic comparisons of mixture models
- Abstract: Abstract
Let
\(X_1,\ldots ,X_n\)
be a random sample from a distribution function
\(F\)
that denote lifetimes of
\(n\)
components of a coherent system. Suppose the system fails at
\(X_{k:n}\)
, the
\(k\)
th order statistic of
\(X\)
’s, since we are not aware of the exact time at which the system has been failed, the residual lifetimes of the remaining
\(n-k\)
components, denoted by
\(X^{(k)}_1,\ldots ,X^{(k)}_{n-k}\)
, are no longer independent but exchangeable. In this paper, multivariate stochastic comparisons of two vectors of lifetimes of the remaining components in the two sample problems are studied. Some sufficient conditions under which multivariate mixture models are compared stochastically with respect to the multivariate likelihood ratio ordering, the multivariate hazard rate ordering and the multivariate reversed hazard rate ordering are provided. These comparisons are done for different choices of the mixed distributions as well as mixing distributions. The new results obtained are applied to compare multivariate mixtures of location models.
PubDate: 2015-11-01
- Abstract: Abstract
Let
\(X_1,\ldots ,X_n\)
be a random sample from a distribution function
\(F\)
that denote lifetimes of
\(n\)
components of a coherent system. Suppose the system fails at
\(X_{k:n}\)
, the
\(k\)
th order statistic of
\(X\)
’s, since we are not aware of the exact time at which the system has been failed, the residual lifetimes of the remaining
\(n-k\)
components, denoted by
\(X^{(k)}_1,\ldots ,X^{(k)}_{n-k}\)
, are no longer independent but exchangeable. In this paper, multivariate stochastic comparisons of two vectors of lifetimes of the remaining components in the two sample problems are studied. Some sufficient conditions under which multivariate mixture models are compared stochastically with respect to the multivariate likelihood ratio ordering, the multivariate hazard rate ordering and the multivariate reversed hazard rate ordering are provided. These comparisons are done for different choices of the mixed distributions as well as mixing distributions. The new results obtained are applied to compare multivariate mixtures of location models.
- Asymptotic results of a nonparametric conditional cumulative distribution
estimator in the single functional index modeling for time series data
with applications- Abstract: Abstract
In this paper, we treat nonparametric estimation of the conditional cumulative distribution with a scalar response variable conditioned by a functional Hilbertian regressor. We establish asymptotic normality and uniform almost complete convergence rates of the conditional cumulative distribution estimator for dependent variables, linked semiparametrically by the single index structure. Furthermore, we provide some applications and simulations to illustrate our methodology.
PubDate: 2015-10-22
- Abstract: Abstract
In this paper, we treat nonparametric estimation of the conditional cumulative distribution with a scalar response variable conditioned by a functional Hilbertian regressor. We establish asymptotic normality and uniform almost complete convergence rates of the conditional cumulative distribution estimator for dependent variables, linked semiparametrically by the single index structure. Furthermore, we provide some applications and simulations to illustrate our methodology.
- Semiparametric estimation of a zero-inflated Poisson regression model with
missing covariates- Abstract: Abstract
Zero-inflated Poisson (ZIP) regression models have been widely used to study the effects of covariates in count data sets that have many zeros. However, often some covariates involved in ZIP regression modeling have missing values. Assuming that the selection probability is known or unknown and estimated via a non-parametric method, we propose the inverse probability weighting (IPW) method to estimate the parameters of the ZIP regression model with covariates missing at random. The asymptotic properties of the proposed estimators are studied in detail under certain regularity conditions. Both theoretical analysis and simulation results show that the semiparametric IPW estimator is more efficient than the true weight IPW estimator. The practical use of the proposed methodology is illustrated with data from a motorcycle survey of traffic regulations conducted in 2007 in Taiwan by the Ministry of Transportation and Communication.
PubDate: 2015-10-16
- Abstract: Abstract
Zero-inflated Poisson (ZIP) regression models have been widely used to study the effects of covariates in count data sets that have many zeros. However, often some covariates involved in ZIP regression modeling have missing values. Assuming that the selection probability is known or unknown and estimated via a non-parametric method, we propose the inverse probability weighting (IPW) method to estimate the parameters of the ZIP regression model with covariates missing at random. The asymptotic properties of the proposed estimators are studied in detail under certain regularity conditions. Both theoretical analysis and simulation results show that the semiparametric IPW estimator is more efficient than the true weight IPW estimator. The practical use of the proposed methodology is illustrated with data from a motorcycle survey of traffic regulations conducted in 2007 in Taiwan by the Ministry of Transportation and Communication.
- 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: 2015-10-01
- 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.
- 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: 2015-10-01
- 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 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: 2015-10-01
- 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.
- Fisher information in censored samples from folded and unfolded
populations- Abstract: Abstract
Fisher information (FI) forms the backbone for many parametric inferential procedures and provides a useful metric for the design of experiments. The purpose of this paper is to suggest an easy way to compute the FI in censored samples from an unfolded symmetric distribution and its folded version with minimal computation that involves only the expectations of functions of order statistics from the folded distribution. In particular we obtain expressions for the FI in a single order statistic and in Type-II censored samples from an unfolded distribution and the associated folded distribution. We illustrate our results by computing the FI on the scale parameter in censored samples from a Laplace (double exponential) distribution in terms of the expectations of special functions of order statistics from exponential samples. We discuss the limiting forms and illustrate applications of our results.
PubDate: 2015-10-01
- Abstract: Abstract
Fisher information (FI) forms the backbone for many parametric inferential procedures and provides a useful metric for the design of experiments. The purpose of this paper is to suggest an easy way to compute the FI in censored samples from an unfolded symmetric distribution and its folded version with minimal computation that involves only the expectations of functions of order statistics from the folded distribution. In particular we obtain expressions for the FI in a single order statistic and in Type-II censored samples from an unfolded distribution and the associated folded distribution. We illustrate our results by computing the FI on the scale parameter in censored samples from a Laplace (double exponential) distribution in terms of the expectations of special functions of order statistics from exponential samples. We discuss the limiting forms and illustrate applications of our results.
- 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: 2015-10-01
- 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.
- One-sample Bayesian prediction intervals based on progressively type-II
censored data from the half-logistic distribution under progressive stress
model- Abstract: Abstract
Based on progressively type-II censored sample, we discuss Bayesian interval prediction under progressive stress accelerated life tests. The lifetime of a unit under use condition stress is assumed to follow the half-logistic distribution with a scale parameter satisfying the inverse power law. Prediction bounds of future order statistics are obtained. A simulation study is performed and numerical computations are carried out, based on two different progressive censoring schemes. The coverage probabilities and average interval lengths of the confidence intervals are computed via a Monte Carlo simulation.
PubDate: 2015-10-01
- Abstract: Abstract
Based on progressively type-II censored sample, we discuss Bayesian interval prediction under progressive stress accelerated life tests. The lifetime of a unit under use condition stress is assumed to follow the half-logistic distribution with a scale parameter satisfying the inverse power law. Prediction bounds of future order statistics are obtained. A simulation study is performed and numerical computations are carried out, based on two different progressive censoring schemes. The coverage probabilities and average interval lengths of the confidence intervals are computed via a Monte Carlo simulation.
- 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: 2015-10-01
- 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.
- Erratum to: Testing structural changes in panel data with small fixed
panel size and bootstrap- PubDate: 2015-09-23
- PubDate: 2015-09-23