Estimation of a semiparametric recursive bivariate probit model in the presence of endogeneity

The classic recursive bivariate probit model is of particular interest to researchers since it allows for the estimation of the treatment effect that a binary endogenous variable has on a binary outcome in the presence of unobservables. In this article, the authors consider the semiparametric version of this model and introduce a model fitting procedure which permits to estimate reliably the parameters of a system of two binary outcomes with a binary endogenous regressor and smooth functions of continuous covariates. They illustrate the empirical validity of the proposal through an extensive simulation study. The approach is applied to data from a survey, conducted in Botswana, on the impact of education on women's fertility. Some studies suggest that the estimated effect could have been biased by the possible endogeneity arising because unobservable confounders (e.g., ability and motivation) are associated with both fertility and education. The Canadian Journal of Statistics 39: 259–279; 2011 © 2011 Statistical Society of Canada     

Efficient estimation for the proportional hazards model with competing risks and current status data

The proportional hazards model is the most commonly used model in regression analysis of failure time data and has been discussed by many authors under various situations (Kalbfleisch & Prentice, 2002. The Statistical Analysis of Failure Time Data, Wiley, New York). This paper considers the fitting of the model to current status data when there exist competing risks, which often occurs in, for example, medical studies. The maximum likelihood estimates of the unknown parameters are derived and their consistency and convergence rate are established. Also we show that the estimates of regression coefficients are efficient and have asymptotically normal distributions. Simulation studies are conducted to assess the finite sample properties of the estimates and an illustrative example is provided. The Canadian Journal of Statistics © 2009 Statistical Society of Canada     

Context and Surrogate Parenting Among Contemporary Grandparents

This paper provides a conceptual discussion of the relationship between the surrogate parenting role of contemporary American grandparents and temporal, developmental, and ethnic/ra- cial contexts of the life course. Grandparents who are surrogate par- ents, either operate as co-parents by assisting their adult children in the rearing of their offspring, or they assume total responsibility for providing the necessary care and socialization their grandchildren re- quire when their parents cannot. The surrogate parenting responsibili- ties of grandparents are hypothesized to be affected by: (1) temporal context, which concerns the sequencing and synchronization of the assumption of surrogate parenting responsibilities by grandparents relative to their age, peer relationships, and other social role responsibilities; (2) developmental context, which focuses on how grand- parents personal development is hindered or facilitated by the as- sumption of the surrogate parenting role; and (3) ethnic/racial context, which refers to the cultural influences grandparents bring to the surrogate parenting role. The implications of these contexts for the surrogate parenting role of grandparents relative to research, policy, programs, and education are discussed.     

Invariant methods for estimating variance components in mixed linear models 2

The subject of this contribution is to present a survey on new methods for variance component estimation, which appeared in the literature in recent years. Starting from mixed models treated in analysis of variance research work on this field turned over to a more general approach in which the covariance matrix of the vector of observations is assumed to be a unknown linear combination of known symmetric matrices. Much interest has been shown in developing some kinds op optimal estimators for the unknown parameters and most results were obtained for estimators being invariant with respect to a certain group of translations. Therefore we restrict attention to this class of estimates. We will deal with minimum variance unbiased estimators, least squared errors estimators, maximum likelihood estimators. Bayes quadratic estimators and show some relations to the mimimum norm quadratic unbiased estimation principle (MINQUE) introduced by C. R. Rao [20]. We do not mention the original motivation of MINQUE since the otion of minimum norm depends on a measure that is not accepted by all statisticians. Also we do‘nt deal with other approaches like the BAYEsian and fiducial methods which were successfully applied by S. Portnoy [18], P. Rusolph [22], G. C. Tiao, W. Y. Tan [28], M. J. K. Healy [9] and others, although in very special situations, only. Additionally we add some new results and also new insight in the properties of known estimators. We give a new characterization of MINQUE in the class of all estimators, extend explicite expressions for locally optimal quadratic estimators given by C. R. Rao [22] to a slightly more general situation and prove complete class theorems useful for the computation of BAYES quadratic estimators. We also investigate situations in which BAYES quadratic unbiased estimators do'nt change if the distribution of the error terms differ from the normal distribution.     

Data depth‐based nonparametric scale tests

Liu and Singh (1993, 2006) introduced a depth‐based d‐variate extension of the nonparametric two sample scale test of Siegel and Tukey (1960). Liu and Singh (2006) generalized this depth‐based test for scale homogeneity of k ≥ 2 multivariate populations. Motivated by the work of Gastwirth (1965), we propose k sample percentile modifications of Liu and Singh's proposals. The test statistic is shown to be asymptotically normal when k = 2, and compares favorably with Liu and Singh (2006) if the underlying distributions are either symmetric with light tails or asymmetric. In the case of skewed distributions considered in this paper the power of the proposed tests can attain twice the power of the Liu‐Singh test for d ≥ 1. Finally, in the k‐sample case, it is shown that the asymptotic distribution of the proposed percentile modified Kruskal‐Wallis type test is χ² with k ? 1 degrees of freedom. Power properties of this k‐sample test are similar to those for the proposed two sample one. The Canadian Journal of Statistics 39: 356–369; 2011 © 2011 Statistical Society of Canada     

促进大学生基层就业可持续发展的若干思考

为拓宽高校毕业生就业渠道,促进社会主义新农村建设,近年来鼓励和支持高校毕业生到基层就业成为国家的一项重要政策。然而高校毕业生在基层就业存在着周期短、流动量大等结构性失衡问题,现实情况不容乐观。从高校毕业生流向的结构性失衡现象着手,分析影响和制约高校毕业生面向基层就业的主要因素,寻找建立和引导高校毕业生到基层就业的良性机制。     

Unbiased statistical estimation functions for parameters in presence of nuisance parameters

We consider the problem of estimating a vector interesting parameter in the presence of nuisance parameters through vector unbiased statistical estimation functions (USEFs). An extension of the Cramer—Rao inequality relevant to the present problem is obtained. Three possible optimality criteria in the class of regular vector USEFs are those based on (i) the non-negative definiteness of the difference of dispersion matrices (ii) the trace of the dispersion matrix and (iii) the determinant of the dispersion matrix. We refer to these three criteria as M-optimality, T- optimality and D-optimality respectively. The equivalence of these three optimality criteria is established. By restricting the class of regular USEFs considered by Ferreira (1982), we study some interesting properties of the standardized USEFs and establish essential uniqueness of standardized M-optimal USEF in this restricted class. Finally some illustrative examples are included.     

On the optimality of chemical balance weighing designs

In this paper we consider the problem of optimally weighing n objects with N weighings on a chemical balance. Several previously known results are generalized. In particular, the designs shown by Ehlich (1964a) and Payne (1974) to be D-optimal in various classes of weighing designs where N≡2 (mod4) are shown to be optimal with respect to any optimality criterion of Type I as defined in Cheng (1980). Several results on the E-optimality of weighing designs are also given.     

Bivariate control charts for testing x data patterns

A new control chart, called the θ chart, for monitoring the mean of a process with bivariate quality characteristics is proposed. It can identify a rotation, shift or alternation between the subgroups of the process mean. The conventional application of X² chart to identify a sudden shift of the process mean is also expanded to identify a change of the process mean or a change of the process dispersion. Furthermore, when used together, the θ and X² charts could provide further insight into the process.     

An investigation of Kendall's τ modified for censored data with applications

To accommodate testing for independence in bivariate data subject to censoring, several modifications of Kendall's τ are discussed. An extensive computer simulation is done to investigate power properties of these modifications under alternatives of the bivariate normal or bivariate exponential types. The statistics are then applied to available heart pacemaker patient survival data.