A Comparison of Survival Function Estimators in the Koziol–Green Model

In this paper, three competing survival function estimators are compared under the assumptions of the so-called Koziol– Green model, which is a simple model of informative random censoring. It is shown that the model specific estimators of Ebrahimi and Abdushukurov, Cheng, and Lin are asymptotically equivalent. Further, exact expressions for the (noncentral) moments of these estimators are given, and their biases are analytically compared with the bias of the familiar Kaplan–Meier estimator. Finally, MSE comparisons of the three estimators are given for some selected rates of censoring.     

Modified minimax estimation of regression coefficients

Working with the linear regression model (1.1) and having the extraneous information (1.2) about regression coefficients the problem exists how to build estimators (1.3) with the risk (1.4) which enable to utilize the known information in order to reduce their risk as compared with the risk (1.6) of the LSE (1.5). Solution of this problem is known for the positive definite matrix T, namely in form for estimators (1.8) and (1.10).First, it is shown that the proposed estimators (2.6),(2.9) and (2.16) based on psedoinversions of the matrix L represent the solution of the problem of the positive semidefinite matrix T=L'L.Further, the problem of interpretability of estimators in the sense of the inequality (3.1) exists; it is shown that all mentioned estimators are at least partially interpretable in the sense of requirements (3.2) or (3.10).     

Estimation with right‐censored observations under a semi‐Markov model

The semi‐Markov process often provides a better framework than the classical Markov process for the analysis of events with multiple states. The purpose of this paper is twofold. First, we show that in the presence of right censoring, when the right end‐point of the support of the censoring time is strictly less than the right end‐point of the support of the semi‐Markov kernel, the transition probability of the semi‐Markov process is nonidentifiable, and the estimators proposed in the literature are inconsistent in general. We derive the set of all attainable values for the transition probability based on the censored data, and we propose a nonparametric inference procedure for the transition probability using this set. Second, the conventional approach to constructing confidence bands is not applicable for the semi‐Markov kernel and the sojourn time distribution. We propose new perturbation resampling methods to construct these confidence bands. Different weights and transformations are explored in the construction. We use simulation to examine our proposals and illustrate them with hospitalization data from a recent cancer survivor study. The Canadian Journal of Statistics 41: 237–256; 2013 © 2013 Statistical Society of Canada     

农村中小学教师对留守儿童的认知

留守儿童能否得到优质的学校教育,与教师的认知与态度是分不开的。本次调查发现,绝大多数农村中小学教师认为留守儿童与非留守儿童之间存在较大的差异,父母外出后,给孩子成长带了较大的负面影响。因绝大多数农村中小学教师主要是根据他们日常生活中与留守儿童的接触,从而形成对其的总体印象,因此,我们可以认为,农村中小学教师对留守儿童的总体评价与判断是比较可靠的。同时,调查也发现农村基层教育系统尤其是处在农村教育第一线的教师对留守儿童教育问题比较重视,但要警惕将留守儿童＂标签化＂的危险。     

Methods for calculating stationary distribution in linear models of time series

The article deals with methods for computing the stationary marginal distribution in linear models of time series. Two approaches are described. First, an algorithm based on approximation of solution of the corresponding integral equation is briefly reviewed. Then, we study the limit behaviour of the partial sums c ₁ η₁+c ₂ η₂+···+c _n η _n where η _i are i.i.d. random variables and c _i real constants. We generalize procedure of Haiman (1998) [Haiman, G., 1998, Upper and lower bounds for the tail of the invariant distribution of some AR(1) processes. Asymptotic Methods in Probability and Statistics, 45, 723–730.] to an arbitrary causal linear process and relax the assumptions of his result significantly. This is achieved by investigating the properties of convolution of densities.     

Nonparametric regression with cross‐classified responses

In this article, we develop regression models with cross‐classified responses. Conditional independence structures can be explored/exploited through the selective inclusion/exclusion of terms in a certain functional ANOVA decomposition, and the estimation is done nonparametrically via the penalized likelihood method. A cohort of computational and data analytical tools are presented, which include cross‐validation for smoothing parameter selection, Kullback–Leibler projection for model selection, and Bayesian confidence intervals for odds ratios. Random effects are introduced to model possible correlations such as those found in longitudinal and clustered data. Empirical performances of the methods are explored in simulation studies of limited scales, and a real data example is presented using some eyetracking data from linguistic studies. The techniques are implemented in a suite of R functions, whose usage is briefly described in the appendix. The Canadian Journal of Statistics 39: 591–609; 2011. © 2011 Statistical Society of Canada     

Quadratic estimation in mixed linear models with two variance components

Explicit expressions for Bayes invariant quadratic estimates, biased and unbiased, are presented and proved to cover the entire class of admissible estimates in the considered classes. An unbalanced genetic model is studied for demonstration.     

An infinite class of PBIB designs

In this paper, an infinite class of partially balanced incomplete block (PBIB) designs of m+1 associate classes is constructed through the use of a series of row-orthogonal matrices known as partially balanced orthogonal designs (PBOD) of m-associate classes. For the purpose, a series of PBOD is obtained through a method described herein. An infinite class of regular GD designs is also reported.