Effect of reporting bias in the analysis of spontaneous reporting data

It is well‐known that a spontaneous reporting system suffers from significant under‐reporting of adverse drug reactions from the source population. The existing methods do not adjust for such under‐reporting for the calculation of measures of association between a drug and the adverse drug reaction under study. Often there is direct and/or indirect information on the reporting probabilities. This work incorporates the reporting probabilities into existing methodologies, specifically to Bayesian confidence propagation neural network and DuMouchel's empirical Bayesian methods, and shows how the two methods lead to biased results in the presence of under‐reporting. Considering all the cases to be reported, the association measure for the source population can be estimated by using only exposure information through a reference sample from the source population. Copyright © 2014 John Wiley & Sons, Ltd.     

Inequalities involving expectations of selected functions in reliability theory to characterize distributions

Recently, authors have studied inequalities involving expectations of selected functions, viz. failure rate, mean residual life, aging intensity function, and log-odds rate which are defined for left truncated random variables in reliability theory to characterize some well-known distributions. However, there has been growing interest in the study of these functions in reversed time (X ? x, instead of X > x) and their applications. In the present work we consider reversed hazard rate, expected inactivity time, and reversed aging intensity function to deal with right truncated random variables and characterize a few statistical distributions.     

Bayesian pitman closeness

The present article brings in the notion of Posterior Pitman Closeness (PPC) in contrast to the usual Pitman Closeness (PC) criterion. Unlike the PC criterion, the PPC criterion does not suffer from lack of transitivity. Also, a posterior median is usually a posterior Pitman closest estimator of the parameter of interest. Examples are provided to illustrate these ideas. Also, some multivariate analogs of these results are presented.     

Nonparametric empirical bayes estimation of certain funtionals

For estimating functionals of the form ∫∫φ(x,y)dF(x) dF(y), nonparametric empirical Bayes estimators are developed which are competitors of the classical U-statistics. Asymptotic optimality of the proposed estimators is proved     

Maximum likelihood estimation foe two parameter exponentials under type I censoring

The paper considers maximum likelihood estimation of the location parameters and the failure rates of two parameter exponentials under type I censoring. Both the one and two sample cases are considered. It turns out that by debiasing the maximum likelihood estimators of the location parameters, one can achieve asymptotically 50% mean squared error reduction.     

Sequential point estimation of the means of u-statistics in finite population sampling

In simple random sampling without replacement from a finite population, sequential point estimators of the means of U-statistics are proposed. The proposed procedure is shown to be asymptotically risk efficient in the sense of Starr (Ann. Math. Statist. (1966), 1173-1185)     

Sequential shrinkage estimation of independent normal means with unkown variances

The Paper considers estimation of the p(> 3)-variate normal mean when the variance-covariance matrix is diagonal with unknown diagonal elements. A class of James-Stein estimators is developed, and is compared with the sample mean under an empirical minimax stopping rule. Asymptotic risk expansions are provided for both the sequential sample mean and the sequential James-Stein estimators. It is shown that the James-Stein estimators dominate the sample mean in a certain asymptotic sense.     

Bias corrected empirical Bayes confidence intervals for the selected mean

Empirical Bayes (EB) methods are very useful for post selection inference. Following Datta et al. (2002 Datta, G. S., M. Ghosh, D. D. Smith, and P. Lahiri. 2002. On an asymptotic theory of conditional and unconditional coverage probabilities of empirical Bayes confidence intervals. Scandinavian Journal of Statistics 29:139–52.[Crossref], [Web of Science ®] , [Google Scholar]), we construct EB confidence intervals for the selected population mean. The EB intervals are adjusted to achieve the target coverage probabilities asymptotically up to the second order. Both unconditional coverage probabilities of EB intervals and corresponding probabilities conditional on ancillary statistics are found.     

A study of demographic trends in West Bengal during 1901–1950

From time to time attempts have been made to determine the trends of fertility of the Indian population. Actuarial analyses which have been undertaken in this connection, published in the Census Reports and elsewhere² are admitted to be in the nature of makeshifts. The difficulty with such reconstructions is that while they may adequately represent the trends and tendencies in a fairly homogenous region or, over a short period of time, they may be misleading when the region covered is too large, or the period considered is too long. Studies covering India as a whole have in most cases to depend largely on the Census. But in the Census returns the errors in age and other details are very large and the conclusions thus depend to a great extent on the power of the particular smoothing formula which is used. But although these facts are well known, demographers dealing with India rely too often on such data for drawing conclusions not only about narrow time periods or small regions, but also for determining fertility trends and differentials over a long period and for the country as a whole.