Comparison to control in logistic regression

We are interested in comparing logistic regressions for several test treatments or populations with a logistic regression for a standard treatment or population. The research was motivated by some real life problems, which are discussed as data examples. We propose a step-down likelihood ratio method for declaring differences between the test treatments or populations and the standard treatment or population. Competitors based on the sequentially rejective Bonferroni Wald statistic, sequentially rejective exact Wald statistic and Reiers?l's statistic are also discussed. It is shown that the proposed method asymptotically controls the probability of type I error. A Monte Carlo simulation shows that the proposed method performs well for relatively small sample sizes, outperforming its competitors.     

Pattern of clustering of menopausal problems: A study with a Bengali Hindu ethnic group

Abstract

We attempted to find out how menopausal problems cluster with each other. The study was conducted among a group of women belonging to a Bengali-speaking Hindu ethnic group of West Bengal, a state located in Eastern India. We recruited 1,400 participants for the study. Information on sociodemographic aspects and menopausal problems were collected from these participants with the help of a pretested questionnaire. Results of cluster analysis showed that vasomotor, vaginal, and urinary problems cluster together, separately from physical and psychosomatic problems.     

The matching, birthday and the strong birthday problem: a contemporary review

This article provides a contemporary exposition at a moderately quantitative level of the distribution theory associated with the matching and the birthday problems. A large number of examples, many not well known, are provided to help a reader have a feeling for these questions at an intuitive level.     

Efficient Bayesian shape-restricted function estimation with constrained Gaussian process priors

Statistics and Computing - This article revisits the problem of Bayesian shape-restricted inference in the light of a recently developed approximate Gaussian process that admits an equivalent...     

High-dimensional posterior consistency of the Bayesian lasso

ABSTRACT

This paper considers posterior consistency in the context of high-dimensional variable selection using the Bayesian lasso algorithm. In a frequentist setting, consistency is perhaps the most basic property that we expect any reasonable estimator to achieve. However, in a Bayesian setting, consistency is often ignored or taken for granted, especially in more complex hierarchical Bayesian models. In this paper, we have derived sufficient conditions for posterior consistency in the Bayesian lasso model with the orthogonal design, where the number of parameters grows with the sample size.     

Allocating multiple estates among agents with single-peaked preferences

We consider the problem of allocating multiple social endowments (estates) of a perfectly divisible commodity among a group of agents with single-peaked preferences when each agent’s share can come from at most one estate. We inquire if well-known single-estate rules, such as the Uniform rule, the Proportional rule or the fixed-path rules can be coupled with a matching rule so as to achieve efficiency in the multi-estate level. On the class of problems where all agents have symmetric preferences, any efficient single-estate rule can be extended to an efficient multi-estate rule. If we allow asymmetric preferences however, this is no more the case. For nondictatorial single-estate rules that satisfy efficiency, strategy proofness, consistency, and resource monotonicity, an efficient extension to multiple estates is impossible. A similar impossibility also holds for single-estate rules that satisfy efficiency, peak-only, and a weak fairness property. We would like to express our gratitude to Bhaskar Dutta, Semih Koray, Hervé Moulin, and Yuntong Wang as well as an associate editor and two anonymous referees of this journal for detailed comments and suggestions. We also thank the seminar participants at Bilkent University, Indian Statistical Institute, Bilgi University, University of Warwick, ASSET 2003, and BWED XXVI.     

On some problems arising from Professor Rawls' conception of distributive justice

This paper is concerned with two specific aspects of Professor Rawls' conception of distributive justice. In Section I Rawls' controversial difference principle is discussed in the context of individual decision under uncertainty, as well as the problem of interpersonal comparison of utilities. It is noted that, contrary to some recent accounts, Rawls' conception of the original position is considerably different from that to be found in the works of Harsanyi. In Section II an attempt is made to articulate in a precise way Rawls' intergenerational savings principle. While it is noted that the Rawlsian savings rule possesses a number of attractive properties, it is demonstrated that it conflicts with the principle of intertemporal Pareto efficiency.This is a revised and expanded version of the text of a lecture delivered at the Moral Sciences Club of the University of Cambridge in February, 1973. I would like to acknowledge the many instructions that I have received on the matters discussed in this paper from Kenneth Arrow, Simon Blackburn, Frank Hahn, Philip Pettit, John Rawls, Abhijit Sen, Amartya Sen, and Robert Solow. While I doubt very much if any of these gentlemen would agree with all that I assert in this paper, I hope that each agrees with some of the propositions madehere.     

Non-identifiable parametric probability models and reparametrization

Identifiability is a primary assumption in virtually all classical statistical theory. However, such an assumption may be violated in a variety of statistical models. We consider parametric models where the assumption of identifiability is violated, but otherwise satisfy standard assumptions. We propose an analytic method for constructing new parameters under which the model will be at least locally identifiable. This method is based on solving a system of linear partial differential equations involving the Fisher information matrix. Some consequences and valid inference procedures under non-identifiability have been discussed. The method of reparametrization is illustrated with an example.