Shanti S. Gupta

Rajshahi University of Engineering and Technology

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Deng-Yuan Huang

Dayeh University

TaChen Liang

Wayne State University

S. Panchapakesan

Simon Fraser University

Raj Senani

Netaji Subhas University of Technology

Klaus J. Miescke

University of Illinois Chicago

Jason C. Hsu

Taipei Medical University

Milton Sobel

University of California, Santa Barbara

D. R. Bhaskar

Delhi Technological University

Lii-Yuh Leu

St. John's University

Gary C. McDonald

Oakland University

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Guru Gobind Singh Indraprastha University

University of Illinois Chicago

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Rajshahi University of Engineering and Technology

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Southern Illinois University Carbondale

Delhi Technological University

National Central University

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SOME ASPECTS OF SELECTION AND RANKING PROCEDURES WITH APPLICATIONS

Shanti S. Gupta W. J. Studden

Abstract : The purpose of the paper is to discuss the problems of ranking and selection in a more or less unified form and suggest some applications to problems in reliability. More specifically, the authors discuss the problem of selecting a sub-set of k populations or processes which in some sense is a best subset.

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A System of Inequalities for the Incomplete Gamma Function and the Normal Integral

The Annals of Mathematical Statistics (1965)

Shanti S. Gupta Mrudulla N. Waknis

In this paper a new set of inequalities and bounds for the incomplete gamma function are obtained. These inequalities and bounds are based on continued fraction expansions of the incomplete gamma function (Sections 2 and 3). Comparisons between the two sets of inequalities and some other known inequalities are made (Section 4). Bounds are also obtained for the Mills' ratio for the normal integral (Section 5) and an analogue of Mills' ratio (Section 6) for the gamma distribution. Some other applications of these bounds to distribution theory problems arising in multiple decision theory are described (Section 6).

Incomplete gamma function

Section (typography)

10.1214/aoms/1177700278

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Selection Procedures for Optimal Subsets of Regression Variables.

Shanti S. Gupta Deng-Yuan Huang C L Chang

Abstract : This paper deals with selection of an optimal subset of variables in a linear regression model. Based on the criterion of expected residual mean squares, we reject inferior regression models. The derivation of the rule is different from those of the earlier papers in that here we use the simultaneous tests of a family of hypotheses. Using real data, an example is provided to illustrate the application of the proposed procedure. (Author)

Regression diagnostic

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On the Problem of Finding the Largest Normal Mean under Heteroscedasticity

Shanti S. Gupta Klaus J. Miescke

Abstract : Let P sub 1,..., P sub k be k approximately equal to 3 given normal populations with unknown means theta sub 1,..., theta sub k, and a common known variance sigma squared. Let X sub 1,..., X sub k be the sample means of k independent samples o sizes n sub 1,...,n sub k from these populations. To find the population with the largest mean, one usually applies the natural rule d sub N, which selects in terms of the largest sample mean. In this paper, the performance of this rule is studied under 0 - 1 loss. It is shown that d sub n is minimax if and only if n sub 1 = ...= n sub k. d sub N is seen to perform weakly whenever the parameters theta sub 1,..., theta sub k are close together. Several alternative selection rules are derived in a Bayesian approach which seem to be reasonable competitors to d sub N, worth comparing with d sub N in a future simulation study.

10.21236/ada172023

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Citations (23)

Hierarchical Bayesian Selection Procedures for the Best Binomial Population

John Deely Shanti S. Gupta

Abstract : In this paper a hierarchical Bayesian model is adopted to derive selection procedures for selecting the best of k binomial parameters, say the probability of success corresponding to k different suppliers. This model facilitates the use of prior information in the analysis for both small and large sample sizes. In addition to computing posterior probabilities that the i to the th power supplier is best, this paper presents expressions for deciding how much better a given supplier is relative to the others. Prior information is assumed to begin with exchangeability and can be more informative if the experimenter has other knowledge about the suppliers as a group. A numerical example is given and the paper concludes with remarks about future work.

Binomial (polynomial)

10.21236/ada196651

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Citations (3)

ON BAYES AND EMPIRICAL BAYES TWO-STAGE ALLOCATION PROCEDURES FOR SELECTION PROBLEMS**This research was supported in part by the Office of Naval Research Contract N00014-88-K-0170 and NSF Grants DMS-8606964, DMS-8702620 at Purdue University.

Elsevier eBooks (1989)

Shanti S. Gupta TaChen Liang

Empirical Research

10.1016/b978-0-444-88029-1.50011-3

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Citations (0)

Selecting important independent variables in linear regression models

Journal of Statistical Planning and Inference (1990)

Shanti S. Gupta Deng-Yuan Huang

10.1016/0378-3758(90)90047-x

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Citations (1)

Order Statistics from the Gamma Distribution

Technometrics (1960)

Shanti S. Gupta

This paper deals with order statistics from a gamma or χ2 (Pearson Type III) distribution. Expressions are derived for the moments of an order statistic and for the covariance between two order statistics. A table of moments (about the origin as well as the mean) is presented. Equations are derived which are used to solve for the percentage points of the order statistics and a table of the percentage points is given. The problem of the best linear unbiased estimate of the scale parameter of the distribution which is based on order statistics is, briefly, discussed for the censored (type II) case. The modal value of an order statistic is derived and a table of these values is given for the cases of the smallest and the largest order statistics. Applications 'to life-tests, extreme values, reliability and maintenance are described and illustrated in some cases.

L-moment

Statistic

Table (database)

Scale parameter

10.1080/00401706.1960.10489897

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Citations (132)

EMPIRICAL BAYES RULES FOR SELECTING THE BEST NORMAL POPULATION COMPARED WITH A CONTROL

Statistics & Risk Modeling (1994)

Shanti S. Gupta TaChen Liang Re-Bin Rau

Normal population

10.1524/strm.1994.12.2.125