Communications in Statistics: Theory and Methods

Dimitrakopoulou, Theodora; Adamidis, Konstantinos; Loukas, Sotirios

doi: 10.1080/03610926.2010.535628pmid: N/A

In this article four derivations are presented, for an absolutely continuous bivariate extension of the Extended Exponential-Geometric distribution (EEG) introduced by Adamidis et al. (2005). Three of these derivations are based on “shock models” and one is based on the assumption of a two component system working in a varying environment. Marginal and conditional distributions are obtained and their corresponding survival and hazard functions are calculated. The dependence in the proposed bivariate distributions is evaluated by means of the Pearson correlation coefficient.

Rukhin, Andrey; Priebe, Carey E.

doi: 10.1080/03610926.2010.533237pmid: N/A

Let p ∈ (0, 1) and let n ∈ ℕ. Moreover, let s ∈ (p, 1], let m = m(n) be a positive, integer-valued function of n with for some positive integer k. We define ER(n, p) to be the random graph model on n vertices where each edge is independently included in the graph with probability p. We also define κ(n, p, m, s) to be the random graph model on n vertices where edges are included independently; however, there is a fixed subset of m vertices for which each of the edges are included with probability s (and the remaining edges are each included with probability p). Let G = (V, E) denote a graph on n vertices. For any vertex v ∈ V, let N[v] denote the set of neighbors of v along with v itself, and let Ω[v] denote the induced subgraph on this neighborhood of vertices. The aim of this article is to determine the limiting distribution (n → ∞) of the graph scan statistic We prove that is asymptotically Gumbel in both the ER(n, p) and κ(n, p, m, s) random graph models.

Gupta, Arindam; Bhattacharya, Sabyasachi; Chattyopadhyay, Asis Kumar

doi: 10.1080/03610926.2010.538794pmid: N/A

The logistic model has some limitations when applied to the sparse census data sets, typically available for developing countries. In such a situation, the relative growth rates (RGR) exhibit some unusual trends which are different from the common decreasing trend of logistic law. To explain such irregular trends we extend the logistic law by incorporating nonlinear positive and negative feedback terms. We performed RGR modelling as a function of time, as the size covariate model is not analytically solvable and the underlying model is better identifiable in the former case. It can also detect the demographic phase change point of developing country.

Wu, Qiang; Sampson, Allan R.

doi: 10.1080/03610926.2010.539745pmid: N/A

Structured means have been used in studying possible covariate effects on responses, whereas patterned covariances deal with random effects, missing data, and differing study designs. In this article, we develop new multivariate models with patterned means and covariance matrices to deal with special structures of the post-mortem brain tissue data collected in the Conte Center for the Neuroscience of Mental Disorders at the University of Pittsburgh. We obtain maximum likelihood estimates via the method of scoring for these new structured models. One-iteration estimators from a consistent starting point are used to derive the asymptotic distributions. The model fitting algorithms, as well as the asymptotic distributions, are examined using simulated data, and are applied to data from post-mortem tissue studies in schizophrenia.

Huang, Zhensheng

doi: 10.1080/03610926.2010.539746pmid: N/A

Xia and Li (1999) proposed the single-index varying-coefficient model (SIVCM), which is frequently used in statistical modeling. However, the inference for the SIVCM has not been very well developed. In this article, our main purpose is to examine whether the generalized likelihood ratio (GLR) test is applicable to the testing problem for the nonparametric parts of the SIVCMs. Under the null hypothesis the newly proposed GLR statistic asymptotically follows the chi-squared distribution with scale constant and degree of freedom independent of the nuisance parameters or functions. A new Wilks phenomenon is unveiled. A simulated example is given to evaluate our proposed methods.

Zhang, Hong; Sa, Ping

doi: 10.1080/03610926.2010.539748pmid: N/A

Sa and Edwards (1993) first proposed the Multiple Comparisons with a Control problem in Response Surface Methodology. They provided an exact solution for one predictor variable and a conservative solution when number of predictor variables is more than one. Merchant et al. (1998) improved the solution for the latter case. This article improves Merchant et al.'s solution for the case of rotatable designs in two predictor variables.

Mahmoudi, Eisa

doi: 10.1080/03610926.2010.539893pmid: N/A

Admissible and minimax estimation of θ r in a subclass of the exponential family with truncated parameter space is considered under squared-log error loss function. We give a necessary and sufficient condition for minimaxity and obtain the classes of new admissible and minimax estimators.

Dabo-Niang, Sophie; Laksaci, Ali

doi: 10.1080/03610926.2010.542850pmid: N/A

Let (X i , Y i ) i=1,…, n be a sequence of strongly mixing random variables valued in ℱ × ℝ, where ℱ is a semi-metric space. We consider the problem of estimating the quantile regression function of Y i given X i . The principal aim of the article is to prove the consistency in L p norm of the proposed kernel estimate. The usefulness of the estimation is illustrated by a real data application where we are interested in forecasting hourly ozone concentration in the south-east of French.

Sheu, Shey-Huei; Chang, Chin-Chih; Chen, Yen-Luan

doi: 10.1080/03610926.2010.542852pmid: N/A

This article presents a generalization of the imperfect sequential preventive maintenance (PM) policy with minimal repair. As failures occur, the system experiences one of two types of failures: a Type-I failure (minor), rectified by a minimal repair; or a Type-II failure (catastrophic) that calls for an unplanned maintenance. In each maintenance period, the system is maintained following the occurrence of a Type-II failure or at age, whichever takes place first. At the Nth maintenance, the system is replaced rather than maintained. The imperfect PM model adopted in this study incorporates with improvement factors in the hazard-rate function. Taking age-dependent minimal repair costs into consideration, the objective consists of finding the optimal PM and replacement schedule that minimize the expected cost per unit time over an infinite time-horizon.

Wei, Chuanhua

doi: 10.1080/03610926.2010.542854pmid: N/A

This article considers statistical inference for partially linear varying-coefficient models when the responses are missing at random. We propose a profile least-squares estimator for the parametric component with complete-case data and show that the resulting estimator is asymptotically normal. To avoid to estimate the asymptotic covariance in establishing confidence region of the parametric component with the normal-approximation method, we define an empirical likelihood based statistic and show that its limiting distribution is chi-squared distribution. Then, the confidence regions of the parametric component with asymptotically correct coverage probabilities can be constructed by the result. To check the validity of the linear constraints on the parametric component, we construct a modified generalized likelihood ratio test statistic and demonstrate that it follows asymptotically chi-squared distribution under the null hypothesis. Then, we extend the generalized likelihood ratio technique to the context of missing data. Finally, some simulations are conducted to illustrate the proposed methods.