Union–intersection principle and constrained statistical inference

Most statistical models arising in real life applications as well as in interdisciplinary research are complex in their designs, sampling plans, and associated probability laws, which in turn are often constrained by inequality, order, functional, shape or other restraints. Optimality of conventional likelihood ratio based statistical inference may not be tenable here, although the use of restricted or quasi-likelihood has spurred in such environments. S.N. Roy's ingenious union–intersection principle provides an alternative avenue, often having some computational advantages, increased scope of adaptability, and flexibility beyond conventional likelihood paradigms. This scenario is appraised here with some illustrative examples, and with some interesting problems of inference on stochastic ordering (dominance) in parametric as well as beyond parametric setups.     

Regression models for analyzing clustered binary and continuous outcomes under an assumption of exchangeability

Scientific experiments commonly result in clustered discrete and continuous data. Existing methods for analyzing such data include the use of quasi-likelihood procedures and generalized estimating equations to estimate marginal mean response parameters. In applications to areas such as developmental toxicity studies, where discrete and continuous measurements are recorded on each fetus, or clinical ophthalmologic trials, where different types of observations are made on each eye, the assumption that data within cluster are exchangeable is often very reasonable. We use this assumption to formulate fully parametric regression models for clusters of bivariate data with binary and continuous components. The regression models proposed have marginal interpretations and reproducible model structures. Tractable expressions for likelihood equations are derived and iterative schemes are given for computing efficient estimates (MLEs) of the marginal mean, correlations, variances and higher moments. We demonstrate the use the ‘exchangeable’ procedure with an application to a developmental toxicity study involving fetal weight and malformation data.     

Some remarks on classical and bayesian reliability estimation of binomial and poisson distributions

The problems of estimating the reliability function and Pr{X₁+...+X_k ≤ Y} are considered. The random variables X’s and Y are assumed to follow binomial and Poisson distributions. Classical estimators available in the literature are discussed and Bayes estimators are derived. In order to obtain the estimators of these parametric functions, the basic role is played by the estimators of factorial moments of the two distributions.     

“The Past in the Present: Mills,Tocqueville and the Necessity of History”

Historical sociology has achieved a reasonable degree of respectability in the discipline, and there is much interesting work being produced. But a pronounced aspect of much of this work is an indifference to the question of the value of studying the past as a way to understanding the present. This article argues that, rather than trying to outdo the historians by producing “better,” more theoretically sophisticated history, sociologists would better advance the case for historical sociology by showing how any particular historical study helps illuminate contemporary concerns. The article draws upon the writings of C. Wright Mills and Alexis de Tocqueville to show not just the need for historical sociology but also as indications of how this might best be done.     

Robustness of tests for directional mean

In this paper we study the robustness of the likelihood ratio, circular mean and circular trimmed mean test functionals in the context of tests of hypotheses regarding the mean direction of circular normal and wrapped normal distributions. We compute the level and power breakdown properties of the three test functionals and compare them. We find that the circular trimmed mean test functional has the best robustness properties for both the above-mentioned distributions. The level and power properties of the test statistics corresponding to these functionals are also studied. Two examples with real data are given for illustration. We also consider the problem of testing the mean direction of the von-Mises–Fisher distribution on the unit sphere and explore the robustness properties of the spherical mean direction and likelihood ratio test functionals.     

The Blended Family Life Cycle

Blended families face unique challenges that differ greatly from those encountered by nuclear families. Societal stereotypes that view blended families as abnormal, taking nuclear family functioning as the prototype for all family units, create a lack of role clarity for each of the members involved. Although many strategies exist with which to help families, many are based on nuclear family systems and thus are inapplicable to blended families. The creation of a blended family life cycle specific to blended family systems could help members of a blended family create a successful family unit as they work with a counselor.     

Challenges and Opportunities in HIV/AIDS Counseling: A Case of Jharkhand

The study highlights the challenges and opportunities in HIV/AIDS counseling. The major challenges are recruiting the right individuals and their capacity building and retention. The finding shows that most of the counselors are not befitting in terms of qualification and experience besides motivation, remuneration, and other issues. The study suggests that to ensure the effective counseling to reverse the epidemic, it is important to focus on such issues through appropriate policy interventions.