Nonparametric estimation for survival data with censoring indicators missing at random

In this paper, we consider the problem of hazard rate estimation in the presence of covariates, for survival data with censoring indicators missing at random. We propose in the context usually denoted by MAR (missing at random, in opposition to MCAR, missing completely at random, which requires an additional independence assumption), nonparametric adaptive strategies based on model selection methods for estimators admitting finite dimensional developments in functional orthonormal bases. Theoretical risk bounds are provided, they prove that the estimators behave well in term of mean square integrated error (MISE). Simulation experiments illustrate the statistical procedure.     

Estimating the distribution function of a transformed random vector

Frequently a random vector Y with known distribution function is readily observed. However, the random variable of interest is a transformation of Y say h(Y), and sample values of h are expensive to evaluate. The objective is to estimate the distribution function of using only a small sample on Y. Four estimators are proposed for use when Y is discrete. A Monte Carlo study of the estimators is presented This estimation problem frequently arises when Y is a parameter in a mathematical programming problem and h(Y) is the optimal objective function value. Two examples of this type are presented.     

Testing separate families of hypotheses using right-censored data

In the present investigation, a series expansion for the cumulants of the x_f-distribution is derived in terms of f-^j up to the order f^-10. As an application a simple Cornish-Fisher-approximation to the noncentrality parameter of noncentral t is given.     

Assessing conditional independence for log-linear poisson models with random effects

In the context of regression rnodels with random effects, repeated response are traditionally assumed to be mutually independent conditional on the random effects. In order to asseess the validity of such an assumption and its impact on parameter inference, we propose an estimating equation methodology where both random eifects and within-subject correlation are modeled. This fllows a subsequent analysis on the statistical sianificance of the conditional correlation. We illustrate this method with the epilepsy data of Thall and Vail (1990), and find our method useh in a proper representation for khe random effect modeling.     

Confidence Intervals for the Median of a Finite Population Based on the Sign Test

This article presents methods for constructing confidence intervals for the median of a finite population under simple random sampling without replacement, stratified random sampling, and cluster sampling. The confidence intervals, as well as point estimates and test statistics, are derived from sign estimating functions which are based on the well-known sign test. Therefore, a unified approach for inference about the median of a finite population is given.     

Extensions of multiple linear regression

Many statistical methods are linked together through their connection with weighted least squares and hence regression. This article reviews these connections, emphasising the iteratively weighted least squares algorithm.     

Projection Mean–Variance Bounds on Expectations of kth Record Values from Restricted Families

We present sharp mean–variance bounds for expectations of kth record values based on distributions coming from restricted families of distributions. These families are defined in terms of convex or star ordering with respect to generalized Pareto distribution. The bounds for expectations of kth record values from DD, DFR, DDA, and DFRA families are special cases of our results. The bounds are derived by application of the projection method.     

Unbiased Estimation of the Distribution Function of an Exponential Population Using Order Statistics with Application in Ranked Set Sampling

In this paper we consider the problem of unbiased estimation of the distribution function of an exponential population using order statistics based on a random sample. We present a (unique) unbiased estimator based on a single, say ith, order statistic and study some properties of the estimator for i = 2. We also indicate how this estimator can be utilized to obtain unbiased estimators when a few selected order statistics are available as well as when the sample is selected following an alternative sampling procedure known as ranked set sampling. It is further proved that for a ranked set sample of size two, the proposed estimator is uniformly better than the conventional nonparametric unbiased estimator, further, for a general sample size, a modified ranked set sampling procedure provides an unbiased estimator uniformly better than the conventional nonparametric unbiased estimator based on the usual ranked set sampling procedure.