Nonparametric estimation of the survival distribution in censored data

Two nonparametric estimators o f the survival distributionare discussed. The estimators were proposed by Kaplan and Meier (1958) and Breslow (1972) and are applicable when dealing with censored data. It is known that they are asymptotically unbiased and uniformly strongly consistent, and when properly normalized that they converge weakly to the same Gaussian process. In this paper, the properties of the estimators are carefully inspected in small or moderate samples. The Breslow estimator, a shrinkage version of the Kaplan-Meier, nearly always has the smaller mean square error (MSE) whenever the truesurvival probabilityis at least 0.20, but has considerably larger MSE than the Kaplan-Meier estimator when the survivalprobability is near zero.     

Maximum likelihood estimation,from doubly censored samples,of the mean of a normal distribution with known coeffucient of variation

Let x be a random variable having the normal distribution with mean μ and variance c²μ², where c is a known constant. The maximum likelihood estimation of μ when the lowest r₁ and the highest r₂ sample values censored have been given the asymptotic variance of the maximum likelihood estimator is obtained.     

A prior-valued estimator applied to multinomial classification

A multinomial classification rule is proposed based on a prior-valued smoothing for the state probabilities. Asymptotically, the proposed rule has an error rate that converges uniformly and strongly to that of the Bayes rule. For a fixed sample size the prior-valued smoothing is effective in obtaining reason¬able classifications to the situations such as missing data. Empirically, the proposed rule is compared favorably with other commonly used multinomial classification rules via Monte Carlo sampling experiments     

A simple method for constructing confounded designs for mixed factorial experiments

This paper presents the sinplesr procedure that uses wodular aryithmetic for constructing confounded designs for mixed factorial experiments. The present procedure and the classical one for confounding in symmetrical factorial experiments are both at the same mathema.tical level. The present procedure is written for

practitioners and is lllustrared with several examples.     

Some conditions for optimality of the almost unbiased estimators of regression coefficients

The purpose of this paper is to examine the asymptotic properties of the operational almost unbiased estimator of regression coefficients which includes almost unbiased ordinary ridge estimator a s a special case. The small distrubance approximations for the bias and mean square error matrix of the estimator are derived. As a consequence, it is proved that, under certain conditions, the estimator is more efficient than a general class of estimators given by Vinod and Ullah (1981). Also it is shown that, if the ordinary ridge estimator (ORE) dominates the ordinary least squares estimator then the almost unbiased ordinary ridge estimator does not dominate ORE under the mean square error criterion.     

Second order efficiency of the ban-estimators for the multinomial family

Rao (1961, 1963) introduced a measure of second order efficiency (s.o.e.) of a best asymptotically normal (BAN) estimator and obtained the s.o.e's of some well known estimators of the parameter of the multinomial family. Koorts (1985) dealt with a calss of BAN estimators and derived the s.o.e, of the estimator belonging to this class. In this paper we derive a general expressiion for the s.o.e. of a BAN estiimator based on its estimating equation.     

Estimating the mean of the selected uniform population

Let π_i(i=1,2,…K) be independent U(0,?_i) populations. Let Y_i denote the largest observation based on a random sample of size n from the i-th population. for selecting the best populaton, that is the one associated with the largest ?_i, we consider the natural selection rule, according to which the population corresponding to the largest Y_i is selected. In this paper, the estimation of M. the mean of the selected population is considered. The natural estimator is positively biased. The UMVUE (uniformly minimum variance unbiased estimator) of M is derived using the (U,V)-method of Robbins (1987) and its asymptotic distribution is found. We obtain a minimax estimator of M for K≤4 and a class of admissible estimators among those of the form cY_max. For the case K = 2, the UMVUE is improved using the Brewster-Zidek (1974) Technique with respect to the squared error loss function L₁ and the scale-invariant loss function L₂. For the case K = 2, the MSE'S of all the estimators are compared for selected values of n and ρ=?₁/(?₁+?₂).     

Estimation of a distribution function bounded by two known distribution functions

The problem of estimation of a cumulative distribution function (cdf), bounded by two known cdf's, is considered. An estimator satisfying the desired restriction has been obtained by suitably adjusting the empirical cdf. Consistency of the adjusted estimator has been established and its mean square error (MSE) has been shown to be smallerthan that of the empirical cdf. The new estimator has been comparedwith the empirical cdf for some special cases.     

Estimation of a finite population total in two-stage and stratified sampling under superpopulation models

Optimal sampling strategies which minimise the expected mean square error for a linear design as well as model-design unbiased estimators for a finite population total for two-stage and stratified sampling are obtained under different superpopu1ation models     

Unbiased estimation of the parameter of a selected binomial population

The problem is to estimate the parameter of a selected binomial population. The selction rule is to choose the population with the greatest number of successes and, in the case of a tie, to follow one of two schemes: either choose the population with the smallest index or randomize among the tied populations. Since no unbiased estimator exists in the above case, we employ a second stage of sampling and take additional observations on the selected population. We find the uniformly minimum variance unbiased estimator (UMVUE) under the first tie break scheme and we prove that no UMVUE exists under the second. We find an unbiased estimator with desirable properties in the case where no UMVUE exists.