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Author

Rahul Mukerjee

Other affiliations: Siemens, Chiba University, Indian Statistical Institute  ...read more
Bio: Rahul Mukerjee is an academic researcher from Indian Institute of Management Calcutta. The author has contributed to research in topics: Frequentist inference & Prior probability. The author has an hindex of 30, co-authored 206 publications receiving 3507 citations. Previous affiliations of Rahul Mukerjee include Siemens & Chiba University.


Papers
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Journal ArticleDOI
TL;DR: In this article, an asymptotic comparison between the locally most mean power unbiased (LMMPU) and Rao's tests in the multi-parameter case is made.

4 citations

Journal ArticleDOI
01 Dec 1990-Metrika
TL;DR: In this article, an approximate theory for the optimality of balanced designs under minimum norm quadratic unbiased estimation of variance components in one-way classified data was developed, where the objective function is to minimize the variance of the balanced design.
Abstract: This paper develops an approximate theory for the optimality of balanced designs under minimum norm quadratic unbiased estimation of variance components in one-way classified data.

4 citations

Journal ArticleDOI
01 Sep 2018
TL;DR: In this article, the optimal design problem for binary vectors with a string property is considered and the robustness to the unknown skewness parameter of the error distribution is explored. And several procedures which entail N-run designs that are highly efficient, if not optimal.
Abstract: We consider the optimal design problem when the design space consists of binary vectors with a string property, i.e., a single stretch of ones. This is done in the framework of second-order least squares estimation which is known to outperform ordinary least squares estimation when the error distribution is asymmetric. Analytical as well as computational results on optimal design measures, under the D- and A-criteria, are obtained. The issue of robustness to the unknown skewness parameter of the error distribution is also explored. Finally, we present several procedures which entail N-run designs that are highly efficient, if not optimal.

4 citations

Journal ArticleDOI
TL;DR: The role of data-dependent priors is investigated and it is seen that the resulting probability matching condition readily allows solutions, in contrast to what happens with data-free priors.

4 citations

Posted Content
TL;DR: In this article, the authors consider causal inference for treatment contrasts from a randomized experiment using potential outcomes in a finite population setting and develop an inferential framework for general mechanisms of assigning experimental units to multiple treatments.
Abstract: This article considers causal inference for treatment contrasts from a randomized experiment using potential outcomes in a finite population setting. Adopting a Neymanian repeated sampling approach that integrates such causal inference with finite population survey sampling, an inferential framework is developed for general mechanisms of assigning experimental units to multiple treatments. This framework extends classical methods by allowing the possibility of randomization restrictions and unequal replications. Novel conditions that are "milder" than strict additivity of treatment effects, yet permit unbiased estimation of the finite population sampling variance of any treatment contrast estimator, are derived. The consequences of departures from such conditions are also studied under the criterion of minimax bias, and a new justification for using the Neymanian conservative sampling variance estimator in experiments is provided. The proposed approach can readily be extended to the case of treatments with a general factorial structure.

3 citations


Cited by
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Journal ArticleDOI
TL;DR: This paper reviews the literature on Bayesian experimental design, both for linear and nonlinear models, and presents a uniied view of the topic by putting experimental design in a decision theoretic framework.
Abstract: This paper reviews the literature on Bayesian experimental design. A unified view of this topic is presented, based on a decision-theoretic approach. This framework casts criteria from the Bayesian literature of design as part of a single coherent approach. The decision-theoretic structure incorporates both linear and nonlinear design problems and it suggests possible new directions to the experimental design problem, motivated by the use of new utility functions. We show that, in some special cases of linear design problems, Bayesian solutions change in a sensible way when the prior distribution and the utility function are modified to allow for the specific structure of the experiment. The decision-theoretic approach also gives a mathematical justification for selecting the appropriate optimality criterion.

1,903 citations

Journal ArticleDOI
TL;DR: In this paper, a review of techniques for constructing non-informative priors is presented and some of the practical and philosophical issues that arise when they are used are discussed.
Abstract: Subjectivism has become the dominant philosophical foundation for Bayesian inference. Yet in practice, most Bayesian analyses are performed with so-called “noninformative” priors, that is, priors constructed by some formal rule. We review the plethora of techniques for constructing such priors and discuss some of the practical and philosophical issues that arise when they are used. We give special emphasis to Jeffreys's rules and discuss the evolution of his viewpoint about the interpretation of priors, away from unique representation of ignorance toward the notion that they should be chosen by convention. We conclude that the problems raised by the research on priors chosen by formal rules are serious and may not be dismissed lightly: When sample sizes are small (relative to the number of parameters being estimated), it is dangerous to put faith in any “default” solution; but when asymptotics take over, Jeffreys's rules and their variants remain reasonable choices. We also provide an annotated b...

1,243 citations

Book
01 Jun 1989
TL;DR: In this article, the authors provide an overview of recent developments in the design and analysis of cross-over trials and present methods for testing for a treatment difference when the data are binary.
Abstract: This chapter provides an overview of recent developments in the design and analysis of cross-over trials. We first consider the analysis of the trial that compares two treatments, A and B, over two periods and where the subjects are randomized to the treatment sequences AB and BA. We make the distinction between fixed and random effects models and show how these models can easily be fitted using modern software. Issues with fitting and testing for a difference in carry-over effects are described and the use of baseline measurements is discussed. Simple methods for testing for a treatment difference when the data are binary are also described. Various designs with two or more treatments but with three or four periods are then described and compared. These include the balanced and partially balanced designs for three or more treatments and designs for factorial treatment combinations. Also described are nearly balanced and nearly strongly balanced designs. Random subject-effects models for the designs with two or more treatments are described and methods for analysing non-normal data are also given. The chapter concludes with a description of the use of cross-over designs in the testing of bioequivalence.

1,201 citations

Journal ArticleDOI
Xinwei Deng1
TL;DR: Experimental design is reviewed here for broad classes of data collection and analysis problems, including: fractioning techniques based on orthogonal arrays, Latin hypercube designs and their variants for computer experimentation, efficient design for data mining and machine learning applications, and sequential design for active learning.
Abstract: Maximizing data information requires careful selection, termed design, of the points at which data are observed. Experimental design is reviewed here for broad classes of data collection and analysis problems, including: fractioning techniques based on orthogonal arrays, Latin hypercube designs and their variants for computer experimentation, efficient design for data mining and machine learning applications, and sequential design for active learning. © 2012 Wiley Periodicals, Inc. © 2012 Wiley Periodicals, Inc.

1,025 citations

Journal ArticleDOI
TL;DR: It is shown that UD's have many desirable properties for a wide variety of applications and the global optimization algorithm, threshold accepting, is used to generate UD's with low discrepancy.
Abstract: A uniform design (UD) seeks design points that are uniformly scattered on the domain. It has been popular since 1980. A survey of UD is given in the first portion: The fundamental idea and construction method are presented and discussed and examples are given for illustration. It is shown that UD's have many desirable properties for a wide variety of applications. Furthermore, we use the global optimization algorithm, threshold accepting, to generate UD's with low discrepancy. The relationship between uniformity and orthogonality is investigated. It turns out that most UD's obtained here are indeed orthogonal.

825 citations