Predictive estimation of population mean in two-phase sampling

ABSTRACT

The present investigation deals with the problem of estimation of population mean in two-phase sampling. In the presence of two auxiliary variables, some classes of estimators have been proposed through predictive approach. Properties of the proposed classes of estimators have been studied, and the unbiased versions of these estimators along with their approximate variance expressions are obtained under simple random sampling without replacement scheme. The respective optimum strategies of the proposed estimators are discussed, and their empirical and graphical comparisons with some contemporary estimators of population mean have been made. Suitable recommendations to the survey practitioner are given.     

On an ethical cum optimal adaptive allocation design

In the present work, we formulate a two-treatment single period two-stage adaptive allocation design for achieving larger allocation proportion to the better treatment arm in the course of the trial with increased precision of the parameter estimator. We examine some properties of the proposed rule and compare it with some of the existing allocation rules and report substantial gain in efficiency with a considerably larger number of allocations to the better treatment even for moderate sample sizes.     

Covariate Classification Using Dependent Samples

The two-population classification problem using dependent samples is extended when covariates are available for classification. Analysis is done using a conditional model, under a multivariate normal set-up, given the covariates. The conditional model considered here includes the parameter structure relevant to growth models. Likelihood ratio or plug-in likelihood ratio classification rules are derived depending on the knowledge of the parameters in the model. For exact distribution of the classification statistics, they are reduced to forms suitable for application of standard results.     

Crossover design in clinical trials for binary response

In this paper, we consider a binary response model for the analysis of the two-treatment, two-period and four-sequence crossover design. We have introduced intra-patient drug dependency parameter in the model and provide two tests for the hypothesis of equality of treatment effects. We employ Monte Carlo simulation to compare our tests and a test that works under parallel design on the basis of type I error rate and power. We find that our procedures are dominant over the competitor with respect to power. Finally, we use a data set to illustrate the applicability of our procedure.     

Two-treatment covariate-dependent response adaptive allocation design for dichotomous response

In the present work we use ridit, a measure comparing two discrete random variables, to develop a two-treatment response adaptive allocation technique in the presence of a stochastic prognostic factor. Various exact and asymptotic performance measures of the proposed technique are obtained and are compared with that of the existing techniques.     

Controlling Type-I Error Rate in Monitoring Structural Changes Using Partially Sequential Procedures

In the present article, we develop some asymptotically power on partially sequential nonparametric tests for monitoring structural changes. Our test procedures are based on Wilcoxon score. We use the idea of curved stopping boundaries. We derive some exact results and perform simulation studies to provide various properties of the tests. We see that one of the proposed procedures significantly controls the Type I error rate. This procedure may be very effective for fluctuation monitoring. We illustrate the procedures by using real life data from the stock market.     

Estimation of ratio of population means in two-occasion successive sampling

ABSTRACT

This article considers the problem of estimation of the ratio of population means at the current occasion based on the samples selected over two occasions. Using auxiliary information on both the occasions, some classes of estimators have been proposed. Properties of the proposed estimators have been studied and their respective optimum replacement strategies are discussed. The gains in efficiency of the proposed classes of estimators over the direct estimator where no past information is used are computed. Theoretical results have been interpreted through empirical studies which are followed by suitable recommendations.     

Sampling strategy for optimal classification into one of two correlated normal populations

A unit ω is to be classified into one of two correlated homoskedastic normal populations by linear discriminant function known as W classification statistic [T.W. Anderson, An asymptotic expansion of the distribution of studentized classification statistic, Ann. Statist. 1 (1973), pp. 964–972; T.W. Anderson, An Introduction to Multivariate Statistical Analysis, 2nd edn, Wiley, New York, 1984; G.J. Mclachlan, Discriminant Analysis and Statistical Pattern Recognition, John Wiley and Sons, New York, 1992]. The two populations studied here are two different states of the same population, like two different states of a disease where the population is the population of diseased patient. When a sample unit is observed in both the states (populations), the observations made on it (which form a pair) become correlated. A training sample is unbalanced when not all sample units are observed in both the states. Paired and also unbalanced samples are natural in studies related to correlated populations. S. Bandyopadhyay and S. Bandyopadhyay [Choosing better training sample for classifying an individual into one of two correlated normal populations, Calcutta Statist. Assoc. Bull. 54(215–216) (2003), pp. 167–180] studied the effect of unbalanced training sample structure on the performance of W statistics in the univariate correlated normal set-up for finding optimal sampling strategy for a better classification rate. In this study, the results are extended to the multivariate case with discussion on application in real scenario.     

A Bayesian adaptive design for two-stage clinical trials with survival data

A randomized two-stage adaptive Bayesian design is proposed and studied for allocation and comparison in a phase III clinical trial with survival time as treatment response. Several exact and limiting properties of the design and the follow-up inference are studied, both numerically and theoretically, and are compared with a single-stage randomized procedure. The applicability of the proposed methodology is illustrated by using some real data.     

Variance estimation for tree-order restricted models

In this article, we discuss the estimation of the common variance of several normal populations with tree-order restricted means. We discuss the asymptotic properties of the maximum-likelihood estimator (MLE) of the variance as the number of populations tends to infinity. We consider several cases of various orders of the sample sizes and show that the MLE of the variance may or may not be consistent or be asymptotically normal.