Improving variance function estimation in semiparametric longitudinal data analysis

We propose an efficient and robust method for variance function estimation in semiparametric longitudinal data analysis. The method utilizes a local log‐linear approximation for the variance function and adopts a generalized estimating equation approach to account for within subject correlations. We show theoretically and empirically that our method outperforms estimators using working independence that ignores the correlations. The Canadian Journal of Statistics 39: 656–670; 2011. © 2011 Statistical Society of Canada     

A new estimator of entropy

Vasicek (1976) proposed an estimator of entropy based on spacings. A new estimator of entropy is proposed. This new estimator is based on local linear regression. Comparisons between this new estimator and Vasicek's estimator are made. The mean square error (MSE) of the new estimator is consistently smaller than the MSE of Vasicek's estimator.     

大学生报考公务员动机的探索性研究

通过对574名报考公务员大学生的问卷调查研究表明：大学生在报考公务员时的动机依次为追求工作待遇、缓解就业压力、追求社会地位、追求社会期望、追求权利资源、实现政治抱负、实现素质与职位匹配,并就不同性别、生源地、学校层次对大学生的报考动机进行了比较分析。     

Local estimation for varying-coefficient models with longitudinal data

Varying-coefficient models are very useful for longitudinal data analysis. In this paper, we focus on varying-coefficient models for longitudinal data. We develop a new estimation procedure using Cholesky decomposition and profile least squares techniques. Asymptotic normality for the proposed estimators of varying-coefficient functions has been established. Monte Carlo simulation studies show excellent finite-sample performance. We illustrate our methods with a real data example.     

Diagnostic tools in generalized Weibull linear regression models

We propose some statistical tools for diagnosing the class of generalized Weibull linear regression models [A.A. Prudente and G.M. Cordeiro, Generalized Weibull linear models, Comm. Statist. Theory Methods 39 (2010), pp. 3739–3755]. This class of models is an alternative means of analysing positive, continuous and skewed data and, due to its statistical properties, is very competitive with gamma regression models. First, we show that the Weibull model induces ma-ximum likelihood estimators asymptotically more efficient than the gamma model. Standardized residuals are defined, and their statistical properties are examined empirically. Some measures are derived based on the case-deletion model, including the generalized Cook's distance and measures for identifying influential observations on partial F-tests. The results of a simulation study conducted to assess behaviour of the global influence approach are also presented. Further, we perform a local influence analysis under the case-weights, response and explanatory variables perturbation schemes. The Weibull, gamma and other Weibull-type regression models are fitted into three data sets to illustrate the proposed diagnostic tools. Statistical analyses indicate that the Weibull model fitted into these data yields better fits than other common alternative models.     

Standard and goodness-of-fit parameter estimation methods for the three-parameter lognormal distribution

A class of goodness-of-fit estimators is found to provide a useful alternative in certain situations to the standard maximum likelihood method which has some undesirable estimation characteristics for estimation from the three-parameter lognormal distribution. The class of goodness-of-fit tests considered include the Shapiro-Wilk and Filliben tests which reduce to a weighted linear combination of the order statistics that can be maximized in estimation problems. The weighted order statistic estimators are compared to the standard procedures in Monte Carlo simulations. Robustness of the procedures are examined and example data sets analyzed.     

Smooth goodness of fit tests for the weibull distribution with singly censored data

The smooth goodness of fit tests are generalized to singly censored data and applied to the problem of testing Weibull (or extreme value) fit. Smooth tests, Pearson-type tests, and the spacings tests proposed by Mann, Schemer, and Fertig (1973) are compared on the basis of local asymptotic relative efficiency with respect to the asymptotic best test against generalized gamma alternatives, The smooth test of order one Is found to be most efficient for the generalized gamma alternatives.     

On shrinkage m-estimators of location parameters

For a general class of continuous ( and marginally symmetric ) inultivariate distributions, based on suitable M-statistics ( involving bounded but possibly discontinuous score generating functions), shrinkage estimators of location are considered. These estimators are based on the James-Stein type rule and incorporates the idea of preliminary test estimation too. The main emphasis is laid on the study of asymptotic tdistributional ) risk properties of these est-innators, and asymptotic tin-) adraissibility results are also studied under fairly general regularity conditions.     

Dependence function for continuous bivariate densities

The notion of cross-product ratio for discrete two-way contingency table is extended to the case of continuous bivariate densities. This results in the “local dependence function” that measues the margin-free dependence between bivariate random variables. Properties and examples of the dependence function are discussed. The bivariate normal density plays a special role since it has constant dependence. Continuous bivariate densities can be constructed by specifying the dependence function along with two marginals in analogy to the construction of two-way contingency tables given marginals and patterns of interaction. The dependence function provides a partial ordering on bivariate dependence.