Showing papers in "Communications in Statistics-theory and Methods in 2010"
TL;DR: In this article, a skewed version of the sinh-normal distribution is introduced, and an extension of the Birnbaum-Saunders model associated with this distribution is presented along with a lifetime analysis based on its hazard rate.
Abstract: In this article, we introduce a skewed version of the sinh-normal distribution and discuss some of its properties. In addition, we characterize an extension of the Birnbaum–Saunders model associated with this distribution from a probabilistic viewpoint along with a lifetime analysis based on its hazard rate. Finally, one of the proposed models is applied to air pollution data in order to illustrate its usefulness.
84 citations
TL;DR: In this paper, a new two-parameter estimator is proposed to overcome the multicollinearity problem, which is a general estimator which includes the ordinary least squares (OLS) estimator, the ridge regression (RR), and the Liu estimator as special cases.
Abstract: This article is concerned with the parameter estimation in linear regression model. To overcome the multicollinearity problem, a new two-parameter estimator is proposed. This new estimator is a general estimator which includes the ordinary least squares (OLS) estimator, the ridge regression (RR) estimator, and the Liu estimator as special cases. Necessary and sufficient conditions for the superiority of the new estimator over the OLS, RR, Liu estimators, and the two-parameter estimator proposed by Ozkale and Kaciranlar (2007) in the mean squared error matrix (MSEM) sense are derived. Furthermore, we obtain the estimators of the biasing parameters and give a numerical example to illustrate some of the theoretical results.
84 citations
TL;DR: A latent block model for a block clustering method, which simultaneously considers the two sets and organize the data into homogeneous blocks, is proposed and various algorithms are provided.
Abstract: Although many clustering procedures aim to construct an optimal partition of objects or, sometimes, variables, there are other methods, called block clustering methods, which simultaneously consider the two sets and organize the data into homogeneous blocks. This kind of method has practical importance in a wide variety of applications such as text and market basket data analysis. Typically, the data that arise in these applications are arranged as a two-way contingency table. Using Poisson distributions, a latent block model for these data is proposed and, setting it under the maximum likelihood approach and the classification maximum likelihood approach, various algorithms are provided. Their performances are evaluated and compared to a simple use of EM or CEM applied separately on the rows and columns of the contingency table.
80 citations
TL;DR: In this article, a simulation study was conducted to compare the performance of double-truncated data with the semi-parametric maximum likelihood estimate (SPMLE) estimator.
Abstract: In many application, statistical data are frequently observed subject to a retrospective sampling criterion resulting in double-truncated data. For double-truncated data, the distribution of lifetime T is observable only when U ≤ T ≤ V, where U and V are the left-truncated and right-truncated time, respectively. Under the assumption of independence between T and (U, V), the nonparametric maximum likelihood estimate (NPMLE) of the distribution function of T (denoted by was developed by Efron and Petrosian (1999). For the special case V = U + d 0, when the distribution of U is parameterized as G(x; θ) and F is left unspecified, a semiparametric MLE estimator of F (denoted by can be obtained using the arguments similar to those of Wang (1989). Further, we can obtain interval estimation for F using the bootstrap method (Qin and Wang, 2001) or the semiparametric likelihood ratio (SLR) method proposed by Li et al. (1997). In this article, a simulation study is conducted to compare the performance between and . ...
76 citations
TL;DR: In this paper, an extended version of the compound Poisson distribution is obtained by compounding the Poisson distributions with the generalized Lindley distribution, and the parameters are estimated using the method of moments and maximum likelihood estimators.
Abstract: An extended version of the compound Poisson distribution is obtained by compounding the Poisson distribution with the generalized Lindley distribution. Estimation of the parameters is discussed using the method of moments and maximum likelihood estimators. Examples are given of the fitting of this distribution to data, and the fit is compared with that obtained using other distributions.
72 citations
TL;DR: In this paper, the authors derived the moment generating functions and the exact distributions of the maximum likelihood estimators (MLEs) of the mean lifetimes of two exponential populations under such a joint progressive type-II censoring.
Abstract: Comparative lifetime experiments are of great importance when the interest is in ascertaining the relative merits of two competing products with regard to their reliability. In this article, we consider two exponential populations and when joint progressive Type-II censoring is implemented on the two samples. We then derive the moment generating functions and the exact distributions of the maximum likelihood estimators (MLEs) of the mean lifetimes of the two exponential populations under such a joint progressive Type-II censoring. We then discuss the exact lower confidence bounds, exact confidence intervals, and simultaneous confidence regions. Next, we discuss the corresponding approximate results based on the asymptotic normality of the MLEs as well as those based on the Bayesian method. All these confidence intervals and regions are then compared by means of Monte Carlo simulations with those obtained from bootstrap methods. Finally, an illustrative example is presented in order to illustrate all the m...
70 citations
TL;DR: In this paper, the authors extend the single Max-EWMA chart to a single double EWMA chart, called the Max-DEWMA Chart, which is based on the maximum of the absolute values of the two DEWMA statistics, one controlling the mean while the other the variance.
Abstract: In this article, we extend the single Max-EWMA chart to a single double EWMA chart, called the Max-DEWMA chart. The statistics of the Max-DEWMA chart are based on the maximum of the absolute values of the two DEWMA statistics, one controlling the mean while the other the variance. We show that the Max-DEWMA chart performs better than the Max-EWMA chart in detecting small and moderate shifts in the mean and/or variance.
68 citations
TL;DR: In this paper, an exponential ratio type estimator for estimating the finite population mean in simple and stratified random sampling is proposed and the properties of the proposed estimator are obtained and comparison is made with some of the existing estimators.
Abstract: In this article, we propose an exponential ratio type estimator for estimating the finite population mean in simple and stratified random sampling. The properties of the proposed estimator are obtained and comparison is made with some of the existing estimators. The proposed estimator is found to perform better than the usual mean, ratio, exponential ratio, traditional regression and Pandy (1980) estimators in simple and stratified random sampling. We use six data sets for simple random sampling case and two data sets for stratified random sampling case to compare the performances of all of the estimators considered here.
57 citations
TL;DR: In this paper, it was shown that the second-order moment of inactivity time determines the distribution uniquely, and that any one partial moment, fractional or integral, of the second order moment uniquely determines a distribution.
Abstract: In this article, it is shown that, apart from the expected inactivity time, the second-order moment of inactivity time determines the distribution uniquely. We also show that any one partial moment, fractional or integral, of inactivity time uniquely determines a distribution. Different properties of the inactivity time of the components of a parallel system, at the system level, have been studied. Stochastic comparisons between two parallel systems based on this is also studied here.
56 citations
TL;DR: The authors proposed three regression-type estimators to overcome the problem of missing data for a study variable, which make optimal use of the available auxiliary information, given the same amount of information.
Abstract: Motivated by a recent work by Kadilar and Cingi (2008), we proposed three regression-type estimators to overcome the problem of missing data for a study variable. The estimators make optimal use of the available auxiliary information. We show that, given the same amount of information, these estimators are simpler and more efficient than those proposed by Kadilar and Cingi. A numerical illustration, performed on three different populations, highlights the efficiency gain from using our proposal. Finally, a suggestion is made regarding the optimal use of auxiliary information in sampling practice.
53 citations
TL;DR: In this article, the authors consider the statistical inference for the mean functions in the two samples problem drawn from functional data sets, in which they assume that functional curves are observed, that is, they consider the test if these two groups of curves have the same mean functional curve when the two groups without noise are observed.
Abstract: Data in many experiments arises as curves and therefore it is natural to use a curve as a basic unit in the analysis, which is in terms of functional data analysis (FDA) Functional curves are encountered when units are observed over time Although the whole function curve itself is not observed, a sufficiently large number of evaluations, as is common with modern recording equipment, is assumed to be available In this article, we consider the statistical inference for the mean functions in the two samples problem drawn from functional data sets, in which we assume that functional curves are observed, that is, we consider the test if these two groups of curves have the same mean functional curve when the two groups of curves without noise are observed The L 2-norm based and bootstrap-based test statistics are proposed It is shown that the proposed methodology is flexible Simulation study and real-data examples are used to illustrate our techniques
TL;DR: In this paper, the authors presented a synthetic control chart for detection of shifts in the process median, which is a combination of sign chart and conforming run-length chart, and the performance evaluation of the proposed chart indicates that the synthetic chart has a higher power of detecting shifts in process median than the Shewhart charts based on sign statistic as well as the classical X-bar chart for various symmetric distributions.
Abstract: This article presents a synthetic control chart for detection of shifts in the process median. The synthetic chart is a combination of sign chart and conforming run-length chart. The performance evaluation of the proposed chart indicates that the synthetic chart has a higher power of detecting shifts in process median than the Shewhart charts based on sign statistic as well as the classical Shewhart X-bar chart for various symmetric distributions. The improvement is significant for shifts of moderate to large shifts in the median. The robustness studies of the proposed synthetic control chart against outliers indicate that the proposed synthetic control chart is robust against contamination by outliers.
TL;DR: The framework proposed here considers two sets of latent variables which are helpful to implement the Bayesian MCMC approach and shows that, for these data sets, the skew-probit links are better than alternative links proposed in the literature.
Abstract: We review several asymmetrical links for binary regression models and present a unified approach for two skew-probit links proposed in the literature. Moreover, under skew-probit link, conditions for the existence of the ML estimators and the posterior distribution under improper priors are established. The framework proposed here considers two sets of latent variables which are helpful to implement the Bayesian MCMC approach. A simulation study to criteria for models comparison is conducted and two applications are made. Using different Bayesian criteria we show that, for these data sets, the skew-probit links are better than alternative links proposed in the literature.
TL;DR: Families of copulas exhibiting different behavior in the tails are introduced in a more flexible way by giving a sufficient condition on ψ that ensures that any distortion of C by means of ψ is again a copula.
Abstract: Given a copula C, we examine under which conditions on an order isomorphism ψ of [0, 1] the distortion C ψ: [0, 1]2 → [0, 1], C ψ(x, y) = ψ{C[ψ−1(x), ψ−1(y)]} is again a copula. In particular, when the copula C is totally positive of order 2, we give a sufficient condition on ψ that ensures that any distortion of C by means of ψ is again a copula. The presented results allow us to introduce in a more flexible way families of copulas exhibiting different behavior in the tails.
TL;DR: In this paper, the authors proposed some alternative estimators for estimating the population mean of a study variable y using information on an auxiliary variable x in the presence of non response under two-phase sampling.
Abstract: This article proposes some alternative estimators for estimating the population mean of a study variable y using information on an auxiliary variable x in the presence of non response under two-phase sampling. The properties of the suggested estimators are given under a large-sample approximation, and the conditions are obtained in which the suggested estimators are better than the conventional unbiased estimators, usual two-phase sampling ratio, and product estimators. In addition, survey cost aspects are discussed under a linear cost function. A real agricultural population is used to present the application of the proposed estimators.
TL;DR: In this article, Monte Carlo experiments are conducted to compare the Bayesian and sample theory model selection criteria in choosing the univariate probit and logit models, and the results show that if data are balanced none of the criteria considered in this article can distinguish the probit or logit model.
Abstract: Monte Carlo experiments are conducted to compare the Bayesian and sample theory model selection criteria in choosing the univariate probit and logit models. We use five criteria: the deviance information criterion (DIC), predictive deviance information criterion (PDIC), Akaike information criterion (AIC), weighted, and unweighted sums of squared errors. The first two criteria are Bayesian while the others are sample theory criteria. The results show that if data are balanced none of the model selection criteria considered in this article can distinguish the probit and logit models. If data are unbalanced and the sample size is large the DIC and AIC choose the correct models better than the other criteria. We show that if unbalanced binary data are generated by a leptokurtic distribution the logit model is preferred over the probit model. The probit model is preferred if unbalanced data are generated by a platykurtic distribution. We apply the model selection criteria to the probit and logit models that li...
TL;DR: In this article, the authors explore properties of the cumulative residual entropy and study conditions under which the CRE of the first-order statistics can uniquely determine the parent distribution, where the Weibull family is characterized through the ratio of the CRE to its expectation.
Abstract: Two different distributions may have equal cumulative residual entropy (CRE), thus a distribution cannot be determined by its CRE. In this article, we explore properties of the CRE and study conditions under which the CRE of the first-order statistics can uniquely determines the parent distribution. Weibull family is characterized through ratio of the CRE of the first-order statistics to its expectation. We have also some bounds for the CRE of residual lifetime of a series system.
TL;DR: In this article, a covariate-adjusted partially linear regression model (CAPLM) is proposed, in which both response and predictor vector can only be observed after being distorted by some multiplicative factors, and an additional variable such as age or period is taken into account.
Abstract: Motivated by covariate-adjusted regression (CAR) proposed by Senturk and Muller (2005) and an application problem, in this article we introduce and investigate a covariate-adjusted partially linear regression model (CAPLM), in which both response and predictor vector can only be observed after being distorted by some multiplicative factors, and an additional variable such as age or period is taken into account. Although our model seems to be a special case of covariate-adjusted varying coefficient model (CAVCM) given by Senturk (2006), the data types of CAPLM and CAVCM are basically different and then the methods for inferring the two models are different. In this article, the estimate method motivated by Cui et al. (2008) is employed to infer the new model. Furthermore, under some mild conditions, the asymptotic normality of estimator for the parametric component is obtained. Combined with the consistent estimate of asymptotic covariance, we obtain confidence intervals for the regression coefficients. Al...
TL;DR: It is proved that the Renyi information between order statistics and parent random variable is distribution free, and it is shown, as expected, the distance is minimum for the median.
Abstract: In this article, we discuss some properties of Renyi entropy and Renyi information of order statistics. Some bounds for Renyi entropy of order statistics are obtained. Also, we relate Renyi entropy ordering of order statistics to Renyi entropy ordering and other well known orderings of parent random variables. Then it is proved that the Renyi information between order statistics and parent random variable is distribution free, and it is shown, as expected, the distance is minimum for the median.
TL;DR: In this paper, Chakraborti and Eryilmaz proposed a nonparametric control chart for the median and other percentiles based on runs of sign statistics above and below the control limits.
Abstract: Nonparametric control charts are considered for the median and other percentiles based on runs of sign statistics above and below the control limits. It is noted that the sign charts are advantageous in certain practical situations. Expressions for the run-length distributions are derived using Markov chain theory; several examples are given. The in-control (IC) and the out-of-control (OOC) performance of these charts are studied and compared to the existing nonparametric Wilcoxon signed-ranked charts of Chakraborti and Eryilmaz (2007) under the normal, the double exponential and the Cauchy distributions, using the average run-length (ARL), the standard deviation of the run-length (SDRL), the false alarm rate (FAR) and some percentiles of the run-length, including the median run-length (MDRL). It is shown that the proposed “runs-rules enhanced” sign charts offer more practically desirable IC ARL (ARL 0) and FAR values and perform better for some heavy-tailed distributions. Some concluding remarks are offered.
TL;DR: In this paper, a new characterization of bivariate copulas is given by using the notion of Dini derivatives, and several examples illustrate the usefulness of this result in the analysis of copulas.
Abstract: A new characterization of bivariate copulas is given by using the notion of Dini derivatives. Several examples illustrate the usefulness of this result.
TL;DR: In this paper, a doubly censored sample from a two-parameter Rayleigh life model was used to derive the predictive distributions for a single future response, the ith future response and several future responses.
Abstract: This article is concerned with making predictive inference on the basis of a doubly censored sample from a two-parameter Rayleigh life model We derive the predictive distributions for a single future response, the ith future response, and several future responses We use the Bayesian approach in conjunction with an improper flat prior for the location parameter and an independent proper conjugate prior for the scale parameter to derive the predictive distributions We conclude with a numerical example in which the effect of the hyperparameters on the mean and standard deviation of the predictive density is assessed
TL;DR: In this article, a multivariate extension of the adaptive exponentially weighted moving average (AEWMA) control chart is proposed, which can detect small and large shifts in the process mean vector effectively.
Abstract: A multivariate extension of the adaptive exponentially weighted moving average (AEWMA) control chart is proposed. The new multivariate scheme can detect small and large shifts in the process mean vector effectively. The proposed scheme can be viewed as a smooth combination of a multivariate exponentially weighted moving average (MEWMA) chart and a Shewhart χ2-chart. The optimal design of the proposed chart is given according to a pre-specified in-control average run length and two shift sizes; a small and large shift each measured in terms of the non centrality parameter. The signal resistance of the newly proposed multivariate chart is also given. Comparisons among the new chart, the MEWMA chart, and the combined Shewhart-MEWMA (S-MEWMA) chart in terms of the standard and worst-case average run length profiles are presented. In addition, the three charts are compared with respect to their worst-case signal resistance values. The proposed chart gives somewhat better worst-case ARL and signal resistance va...
TL;DR: In this article, the authors used the first-passage-time theory for a stochastic process to formulate a dynamic model expressing the human life table data and derived the probability density function for the first exit time.
Abstract: In this article, we use the first-passage-time theory for a stochastic process to formulate a dynamic model expressing the human life table data. The model is derived analytically by using the corresponding Laplace transforms for the probability density function of the stochastic process and then the theory for the hitting time process is used to derive the probability density function for the first exit time. The tangent approximation to one-sided Brownian exit densities is used. The resulting probability density function is applied to mortality data. The stochastic simulation is using the Health State Function proposed with encouraging results.
TL;DR: In this paper, the authors proposed one-step approximations based on the Newton-Raphson algorithm for extreme value under random censoring, which are shown to be close approximation to the ML-estimators.
Abstract: Recently, the topic of extreme value under random censoring has been considered. Different estimators for the index have been proposed (see Beirlant et al., 2007). All of them are constructed as the classical estimators (without censoring) divided by the proportion of non censored observations above a certain threshold. Their asymptotic normality was established by Einmahl et al. (2008). An alternative approach consists of using the Peaks-Over-Threshold method (Balkema and de Haan, 1974; Smith, 1987) and to adapt the likelihood to the context of censoring. This leads to ML-estimators whose asymptotic properties are still unknown. The aim of this article is to propose one-step approximations, based on the Newton-Raphson algorithm. Based on a small simulation study, the one-step estimators are shown to be close approximations to the ML-estimators. Also, the asymptotic normality of the one-step estimators has been established, whereas in case of the ML-estimators it is still an open problem. The proof of our...
TL;DR: In this paper, the authors introduce a new distribution-free Shewhart-type control chart that takes into account the location of a single order statistic of the test sample (such as the median) as well as the number of observations in that test sample that lie between the control limits.
Abstract: In this article, we introduce a new distribution-free Shewhart-type control chart that takes into account the location of a single order statistic of the test sample (such as the median) as well as the number of observations in that test sample that lie between the control limits. Exact formulae for the alarm rate, the run length distribution, and the average run length (ARL) are all derived. A key advantage of the chart is that, due to its nonparametric nature, the false alarm rate and in-control run length distribution are the same for all continuous process distributions, and so will be naturally robust. Tables are provided for the implementation of the chart for some typical ARL values and false alarm rates. The empirical study carried out reveals that the new chart is preferable from a robustness point of view in comparison to a classical Shewhart-type chart and also the nonparametric chart of Chakraborti et al. (2004).
TL;DR: In this paper, several estimators are proposed to estimate θ using ranked set sampling (RSS) data and compared with known estimators based on simple random sample (SRS) data.
Abstract: The problem of making statistical inference about θ =P(X > Y) has been under great investigation in the literature using simple random sampling (SRS) data. This problem arises naturally in the area of reliability for a system with strength X and stress Y. In this study, we will consider making statistical inference about θ using ranked set sampling (RSS) data. Several estimators are proposed to estimate θ using RSS. The properties of these estimators are investigated and compared with known estimators based on simple random sample (SRS) data. The proposed estimators based on RSS dominate those based on SRS. A motivated example using real data set is given to illustrate the computation of the newly suggested estimators.
TL;DR: In this paper, the probabilistic and statistical properties of an parametric extension of the so-called epsilon-skew-normal (ESN) distribution introduced by Mudholkar and Hutson (2000) are investigated.
Abstract: This article is related with the probabilistic and statistical properties of an parametric extension of the so-called epsilon-skew-normal (ESN) distribution introduced by Mudholkar and Hutson (2000), which considers an additional shape parameter in order to increase the flexibility of the ESN distribution. Also, this article concerns likelihood inference about the parameters of the new class. In particular, the information matrix of the maximum likelihood estimators is obtained, showing that it is non singular in the special normal case. Finally, the statistical methods are illustrated with two examples based on real datasets.
TL;DR: In this article, a control chart for the variance of a normal distribution and, equivalently, the coefficient of variation of a log-normal distribution is developed, where a Bayesian approach is used to incorporate parameter uncertainty.
Abstract: This article develops a control chart for the variance of a normal distribution and, equivalently, the coefficient of variation of a log-normal distribution. A Bayesian approach is used to incorporate parameter uncertainty, and the control limits are obtained from the predictive distribution for the variance. We evaluate this control chart by examining its performance for various values of the process variance.
TL;DR: In this paper, a multistage step-down procedure was proposed to adaptively test multiple hypotheses while preserving the family-wise error rate and extending Holm's stepdown procedure to the sequential setting, yielding substantial savings in sample size with small loss in power.
Abstract: Conventional multiple hypothesis tests use step-up, step-down, or closed testing methods to control the overall error rates. We will discuss marrying these methods with adaptive multistage sampling rules and stopping rules to perform efficient multiple hypothesis testing in sequential experimental designs. The result is a multistage step-down procedure that adaptively tests multiple hypotheses while preserving the family-wise error rate and extends Holm's (1979) step-down procedure to the sequential setting, yielding substantial savings in sample size with small loss in power.