Communications in Statistics: Theory and Methods

Wang, Lichun; Singh, Radhey S.

doi: 10.1080/03610926.2010.542853pmid: N/A

In the system of two seemingly unrelated regressions, employing a matrix power series, we show that the two-stage estimator is better than the ordinary least square estimator (OLSE) in terms of the mean square error matrix (MSEM) criterion. The result enriches the existing literature and can be applied to many fields of applications related to economics and statistics.

Jomhoori, Sarah; Fakoor, Vahid; Azarnoosh, Hasanali

doi: 10.1080/03610926.2010.542849pmid: N/A

In some long-term studies, a series of dependent and possibly censored failure times may be observed. Suppose that the failure times have a common continuous distribution function F. A popular stochastic measure of the distance between the density function f of the failure times and its kernel estimate f n is the integrated square error(ISE). In this article, we derive a central limit theorem for the integrated square error of the kernel density estimators under a censored dependent model.

Galea, Manuel; de Castro, Mário

doi: 10.1080/03610926.2010.543301pmid: N/A

The main goal of this article is to consider influence assessment in models with error-prone observations and variances of the measurement errors changing across observations. The techniques enable to identify potential influential elements and also to quantify the effects of perturbations in these elements on some results of interest. The approach is illustrated with data from the WHO MONICA Project on cardiovascular disease.

Roozbeh, M.; Arashi, M.; Gasparini, M.

doi: 10.1080/03610926.2010.542859pmid: N/A

This article is concerned with the problem of multicollinearity in the linear part of a seemingly unrelated semiparametric (SUS) model. It is also suspected that some additional non stochastic linear constraints hold on the whole parameter space. In the sequel, we propose semiparametric ridge and non ridge type estimators combining the restricted least squares methods in the model under study. For practical aspects, it is assumed that the covariance matrix of error terms is unknown and thus feasible estimators are proposed and their asymptotic distributional properties are derived. Also, necessary and sufficient conditions for the superiority of the ridge-type estimator over the non ridge type estimator for selecting the ridge parameter K are derived. Lastly, a Monte Carlo simulation study is conducted to estimate the parametric and nonparametric parts. In this regard, kernel smoothing and cross validation methods for estimating the nonparametric function are used.

Baratpour, S.; Rad, A. Habibi

doi: 10.1080/03610926.2010.542857pmid: N/A

Testing exponentiality has long been an interesting issue in statistical inferences. In this article, we introduce a new measure of distance between two distributions that is similar Kullback–Leibler divergence, but using the distribution function rather than the density function. This new measure is based on the cumulative residual entropy. Based on this new measure, a consistent test statistic for testing the hypothesis of exponentiality against some alternatives is developed. Critical values for various sample sizes determined by means of Monte Carlo simulations are presented for the test statistics. Also, by means of Monte Carlo simulations, the power of the proposed test under various alternative is compared with that of other tests. Finally, we found that the power differences between the proposed test and other tests are not remarkable. The use of the proposed test is shown in an illustrative example.

Sunoj, S. M.; Sreejith, T. B.

doi: 10.1080/03610926.2010.542858pmid: N/A

Recently, reciprocal subtangent has been used as a useful tool to describe the behaviour of a density curve. Motivated by this, in the present article we extend the concept to the weighted models. Characterization results are proved for models viz. gamma, Rayleigh, equilibrium, residual lifetime, and proportional hazards. An identity under weighted distribution is also obtained when the reciprocal subtangent takes the form of a general class of distributions. Finally, an extension of reciprocal subtangent for the weighted models in the bivariate and multivariate cases are introduced and proved some useful results.

Roy, Anuradha; Leiva, Ricardo

doi: 10.1080/03610926.2010.530369pmid: N/A

We study the problem of classification for multivariate repeated measures data with structured correlations on both time and spatial repeated measurements. This is a very important problem in many biomedical as well as in engineering field. Classification rules as well as the algorithm to compute the maximum likelihood estimates of the required parameters are given.

Garcia, Edel

doi: 10.1080/03610926.2011.654037pmid: N/A

In this brief article, we present the Self-Weighting Model (SWM), a new weighting model for statistical analysis. SWM allows within/between-set comparisons, producing estimates with a discriminatory power not found through current weighting strategies. The model is applicable to a wide range of statistical problems for which conditional weighted means are required.

Feigin, P. D.; Lumelskii, Ya. P.; Kryvoshaev, A. V.

doi: 10.1080/03610926.2010.539749pmid: N/A

The problem of calculating approximate confidence limits for the difference between success probability parameters of two Pólya distributions is solved for the first time. We suggest some new methods for determining these approximate confidence limits and consider their application to special cases: namely for the binomial and hypergeometric distributions. The various approximate confidence limits are evaluated and compared.

Vazler, Ivan; Sabo, Kristian; Scitovski, Rudolf

doi: 10.1080/03610926.2010.539750pmid: N/A

We consider the weighted median problem for a given set of data and analyze its main properties. As an illustration, an efficient method for searching for a weighted Least Absolute Deviations (LAD)-line is given, which is used as the basis for solving various linear and nonlinear LAD-problems occurring in applications. Our method is illustrated by an example of hourly natural gas consumption forecast.