Communications in Statistics: Theory and Methods

Bentarzi, M.; Merzougui, M.

doi: 10.1080/03610926.2010.503017pmid: N/A

This article deals with the study of some properties of a mixture periodically correlated autoregressive (MPAR S ) time series model, which extends the mixture time invariant parameter autoregressive (MAR) model, that has recently received a considerable interest from many economic time series analysts, to mixture periodic parameter autoregressive model. The aim behind this extension is to make the model able to capture, in addition to all features captured by the classical MAR model, the periodicity feature exhibited by the autocovariance structure of many encountered financial and environmental time series with eventual multimodal distributions. Our main contribution here is obtaining of the second moment periodically stationary condition for a MPAR S (K; 2,…, 2) model, furthermore the closed-form of the second moment is obtained.

Wang, Dja-Shin; Chou, Chao-Yu; Lin, Yu-Chang

doi: 10.1080/03610926.2011.581780pmid: N/A

The process capability index is a simple quantitative way to assess the capability of a process. To measure the overall yield of a multiple-stream process, Wang et al. (2009) proposed a yield index, denoted by , and then provided a point estimator of for practical industrial applications. In addition to point estimation, interval estimation plays an important role in statistical inference on the process index. In the present paper, we consider the problem of constructing the confidence interval for . First, the sampling distribution of is derived by applying Central Limit Theorem and the method of cumulative distribution functions. Then, the confidence intervals for are obtained using numerical integration by coding a MATLAB computer program. Several useful tables are provided for the purpose of constructing the confidence intervals of . A numerical example is presented to show how these tables may be applied for interval estimation of in a real production process.

Beirlant, Jan; Geffray, Ségolen; Guillou, Armelle

doi: 10.1080/03610921003764258pmid: N/A

Interest is centered on the maximum likelihood (ML) estimators of the parameters of the Generalized Pareto Distribution in an extreme value context. Our aim consists of reducing the bias of these estimates for which no explicit expression is available. To circumvent this difficulty, we prove that these estimators are asymptotically equivalent to one-step estimators introduced by Beirlant et al. (2010) in a right-censoring context. Then, using this equivalence property, we estimate the bias of these one-step estimators to approximate the asymptotic bias of the ML-estimators. Finally, a small simulation study and an application to a real data set are provided to illustrate that these new estimators actually exhibit reduced bias.

Li, Na; Xu, Xingzhong

doi: 10.1080/03610926.2010.503018pmid: N/A

In this article, procedures are proposed to test the hypothesis of equality of two or more regression functions. Tests are proposed by p-values, first under homoscedastic regression model, which are derived using fiducial method based on cubic spline interpolation. Then, we construct a test in the heteroscedastic case based on Fisher's method of combining independent tests. We study the behaviors of the tests by simulation experiments, in which comparisons with other tests are also given. The proposed tests have good performances. Finally, an application to a data set are given to illustrate the usefulness of the proposed test in practice.

Wan, Shuwen; Deng, Xin; Zhang, Biao

doi: 10.1080/03610926.2010.503019pmid: N/A

In the literature, there were only a few reports on goodness-of-fit tests on logistic regression models specifically derived for case-control studies. In this article, we propose a goodness-of-fit test for logistic regression models in stratified case-control studies using an empirical likelihood approach. The proposed statistic is an alternative to the statistic G o , recently proposed by Arbigast and Lin (2005). Simulation results show that the proposed statistic is often slightly more powerful than G o , although their performances are always close to each other. Moreover, implementation of our method is easy since the usual stratified logistic regression procedures in many statistical softwares can be employed. Some asymptotic results and application of the proposed statistic to two real datasets are also presented.

Desmet, L.; Gijbels, I.

doi: 10.1080/03610926.2010.503949pmid: N/A

In Desmet and Gijbels (2009), the problem of curve fitting on functions with peaks was addressed and a method was proposed that was building further on the one used in Gijbels et al. (2007) when dealing with functions that have jump discontinuities. In this article, we propose a common framework for both estimation problems and an integrated procedure where an appropriate diagnostic quantity is a key ingredient. In particular we discuss practical procedure parameter selection considering target functions with an unknown number of irregularities of unknown type. The method is illustrated both on simulated and real life data sets.

Wang, Shuyun; Luan, Yihui; Chang, Qin

doi: 10.1080/03610926.2010.503950pmid: N/A

We consider the problem of variable selection using Bayesian method in high-dimensional linear models, where the number of explanatory variables K n is possibly much larger than the sample size n. In particular, the true regression coefficients vector β* is required sparsity in the sense of , which describes a general situation when all explanatory variables are relevant, but most of them have very small effects. According to Bayesian inference of Wasserman (1998), given a proper prior to propose joint densities f(y, x) of response y and explanatory variables vector x, the posterior-proposed densities are often close to the true density f 0(y, x), for large n. It's the so-called “density consistency”. We aim to prove that in linear models, density consistency can induce regression function consistency, which ensures good performance of variable selection. Especially in the special case of , when some regression coefficients are bounded away from zero while the rest are exactly zero, our method would identify the underlying true model by giving consistent estimate of true regression coefficients vector. We also provide simulation studies and a real data example to demonstrate satisfactory finite-sample performance of our method.

Abeynayake, N. R.; Jaggi, Seema; Varghese, Cini

doi: 10.1080/03610926.2010.505692pmid: N/A

This article deals with the neighbor-balanced block design setting when there are two disjoint sets of treatments, one set consisting of test treatments and the other of control treatments. The interest here is to estimate the contrasts pertaining to test treatments vs. control treatments (with respect to direct and neighbors) with as high precision as possible. Some series of neighbor-balanced block designs for comparing a set of test treatments to a set of control treatments have been developed. The designs obtained are totally balanced in the sense that all the contrasts among test treatments for direct and neighbor effects are estimated with same variance and all the contrasts pertaining to test vs. control for direct and neighbor effects are estimated with the same variance.

Xu, Jianwen; Yang, Hu

doi: 10.1080/03610926.2010.505693pmid: N/A

Sarkar (1992) and Kaç\i ranlar et al. (1999), respectively, proposed the restricted ridge regression estimator (RRE) and restricted Liu estimator (RLE) to combat the well-known multicollinearity problem in linear regression. In this article, the restricted almost unbiased ridge estimator (RAURE) based on the RRE by Sarkar (1992) and the restricted almost unbiased Liu estimator (RAULE) by Kaç\i ranlar et al. (1999) are introduced. The biases and variance matrices of the proposed estimators are derived and compared with the corresponding competitors in literatures. Furthermore, a Monte Carlo evaluation of the estimators is given to illustrate some of the theoretical results.

Szatmari-Voicu, D.

doi: 10.1080/03610926.2010.505690pmid: N/A

We consider first the class of M-estimators of scale that are location-scale equivariant and Fisher consistent at the error distribution of the shrinking contamination neighborhood and derive an expression for the maximal asymptotic mean-squared-error, for a suitably regular score function, followed by a lower bound on it. We next show that the minimax asymptotic mean-squzred-error is attained at an M-estimator of scale with the truncated MLE score function which, when specialized to the Standard Normal error distribution has the form of Huber's Proposal 2. The latter minimax property is also shown to hold for α-trimmed variance as an L-estimator of scale.