Influence Diagnostics of Semiparametric Nonlinear Reproductive Dispersion ModelsChen, Xue-Dong; Tang, Nian-Sheng; Wang, Xue-Ren
doi: 10.1080/03610920903171838pmid: N/A
This article proposes a semiparametric nonlinear reproductive dispersion model (SNRDM) which is an extension of nonlinear reproductive dispersion model and semiparametric regression model. Maximum penalized likelihood estimators (MPLEs) of unknown parameters and nonparametric functions in SNRDMs are presented. Some novel diagnostic statistics such as Cook distance and difference deviance for parametric and nonparametric parts are developed to identify influence observations in SNRDMs on the basis of case-deletion method, and some formulae readily computed with the MPLEs algorithm for diagnostic measures are given. The equivalency of case-deletion models and mean-shift outlier models in SNRDM is investigated. A simulation study and a real example are used to illustrate the proposed diagnostic measures.
Multiple Interval Mapping for Quantitative Trait Loci via EM Algorithm in the Presence of Crossover InterferenceZhou, Ying
doi: 10.1080/03610920903171853pmid: N/A
The rapid advance in molecular biology has made feasible systematic studies of mapping quantitative trait loci (QTL) in experiment organisms. The method of multiple interval mapping provides an appropriate way for mapping QTL using genetic makers. However, crossover interference has not been considered sufficiently in the current QTL mapping in which no crossover interference is assumed, and the length of maker interval is always kept fixed. In this article, we consider the issue of statistical inference in multiple interval mapping for QTL when crossover interference is present. The marker interval can be chosen appropriately in our method without keeping the maker interval lengths fixed in advance, and the asymptotic variance–covariance matrix of the MLEs is also derived. Two simulations are performed to evaluate the proposed method and show the impact of crossover interference to QTL mapping.
Attainability of the Upper Bounds for the Mean Past Lifetime of Parallel System ComponentsRaqab, Mohammad Z.
doi: 10.1080/03610920903180672pmid: N/A
Among reliability systems, one of the basic systems is a parallel system. In this article, we consider a parallel system consisting of n identical components with independent lifetimes having a common distribution function F. Under the condition that the system has failed by time t, with t being 100pth percentile of F(t = F −1(p), 0 < p < 1), we characterize the probability distributions based on the mean past lifetime of the components of the system. These distributions are described in the form of a specific shape on the left of t and arbitrary continuous function on the right tail.
Berry–Esseen Bound for a Class of Normalized L-StatisticsHui, Jiang
doi: 10.1080/03610920903181993pmid: N/A
We study a class of normalized L-statistics based on linear combinations of order statistics divided by its sample mean. Under suitable selection of the its coefficients, we prove that the class of normalized L-statistics converge to the normal distribution with an error rate . Moreover, we also apply our result to Jackson, Gini, and Fortiana–Grané statistics and obtain their Berry–Esseen bound.
Bivariate Aging Properties under Archimedean Dependence StructuresMulero, Julio; Pellerey, Franco
doi: 10.1080/03610920903199987pmid: N/A
Let X = (X, Y) be a pair of lifetimes whose dependence structure is described by an Archimedean survival copula, and let X t = [(X − t, Y − t) | X > t, Y > t] denotes the corresponding pair of residual lifetimes after time t ≥ 0. Multivariate aging notions, defined by means of stochastic comparisons between X and X t , with t ≥ 0, were studied in Pellerey (2008), who considered pairs of lifetimes having the same marginal distribution. Here, we present the generalizations of his results, considering both stochastic comparisons between X t and X t+s for all t, s ≥ 0 and the case of dependent lifetimes having different distributions. Comparisons between two different pairs of residual lifetimes, at any time t ≥ 0, are discussed as well.
Tests for Paired Lifetime Data with Frailty ModelsWang, Zhu
doi: 10.1080/03610920903199995pmid: N/A
We consider the problem of hypothesis testing of the equality of marginal survival distributions observed from paired lifetime data. Usual procedures include the paired t-test, which may perform poor for certain types of data. We propose asymptotic tests based on gamma frailty models with Weibull conditional distributions, and investigate their theoretical properties using large sample theory. For finite samples, we conduct simulations to evaluate the powers of the associated tests. For moderate and less skewed data, the proposed tests are the most powerful among the commonly applied testing procedures. A data example is illustrated to demonstrate the methods.
Methods of Statistical Inference for Median Regression Models with Doubly Censored DataZhou, Xiuqing; Shi, Ningzhong
doi: 10.1080/03610920903200009pmid: N/A
Recently, least absolute deviations (LAD) estimator for median regression models with doubly censored data was proposed and the asymptotic normality of the estimator was established. However, it is invalid to make inference on the regression parameter vectors, because the asymptotic covariance matrices are difficult to estimate reliably since they involve conditional densities of error terms. In this article, three methods, which are based on bootstrap, random weighting, and empirical likelihood, respectively, and do not require density estimation, are proposed for making inference for the doubly censored median regression models. Simulations are also done to assess the performance of the proposed methods.