Subset Selection for the Means of Normal Populations with Unequal Variances PDF Download

Author: Shanti Swarup Gupta
Publisher:
ISBN:
Category : Sampling (Statistics)
Languages : en
Pages : 27

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Author: S. S. Gupta
Publisher:
ISBN:
Category :
Languages : en
Pages : 27

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Author: Lloyd William Koenig
Publisher:
ISBN:
Category : Population
Languages : en
Pages : 224

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Author: Wing-Yue Wong
Publisher:
ISBN:
Category :
Languages : en
Pages : 122

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Book Description
The main purpose of this paper is to propose and study the subset selection approach for some new problems and make contributions. Chapter 1 deals with some selection and ranking procedures for the largest unknown mean of k normal populations with unequal variances. In chapter 2 some nonparametric subset selection procedures based on U-statistics for selecting the largest of the k location parameters are proposed and studied. Chapter 3 discusses some subset selection procedures for Poisson processes. Chapter 4 deals with a class of selection rules for finite schemes. Chapter 5 discusses some subset selection procedures for a negative multinomial distribution. An inverse sampling rule for selecting the cell with largest cell-probability from a multinomial distribution is considered.

Author: Shanti S. Gupta
Publisher:
ISBN:
Category :
Languages : en
Pages : 25

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Let (Pi sub 1), ..., (Pi sub k) be k independent normal populations with means (mu sub 1), ..., (mu sub k) and variances (sigma sub 1, sup 2), ..., (sigma sub k, sup 2), respectively. The authors interest is to select a non-empty subset of the k populations containing the best when the populations are ranked in terms of (i) the means (mu sub i), when (sigma sub i sup 2) = (sigma sup 2), known or unknown, and (ii) the variance (sigma sub i sup 2), when the (mu sub i) are known or unknown. Procedures and results are derived for the case when sample sizes are unequal. The authors also discuss gamma populations with scale parameter, and selection for normal means that are better than control. (Author).

Author: Roger L. Berger
Publisher:
ISBN:
Category :
Languages : en
Pages : 22

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Let X(1), ..., X(k) be observations from populations whose distributions are determined by unknown real parameters theta(1), ..., theta(k). In a subset selection problem, the goal is to select a subset of the populations which includes the population associated with the largest parameter with 'high' probability and includes the other populations with 'low' probability. In this paper, rules are found which are minimax in the class of non-randomized, just, and translation invariant rules when risk is measured by the maximum probability of including a non-best population. These rules are of the form proposed and studied by Gupta in location and scale parameter problems. In many cases, these rules are the unique minimax rule in the class and, hence are also admissible in this class. These results are applied to the normal mean problem with known unequal variances (or unequal sample sizes). Comparison of several proposed rules is made. A rule proposed by Gupta and Huang is found to be minimax. A generalization of the rule, proposed by Gupta and Wong, is likewise minimax. Other rules, proposed by Chen and Dudewicz and Gupta and Huang are shown to be not minimax.

Author: Jean Dickinson Gibbons
Publisher: SIAM
ISBN: 0898714397
Category : Mathematics
Languages : en
Pages : 589

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Provides a compendium of applied aspects of ordering and selection procedures.

Author: Shanti S. Gupta
Publisher:
ISBN:
Category :
Languages : en
Pages : 20

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Book Description
The problem of selecting a subset of k normal populations which includes the population associated with the largest mean is considered for the situation in which the normal populations have a common known coefficient of variation. Subset selection rules based on best asymptotically normal (BAN) estimators of the mean have been studied in the literature and tables based on large sample theory for implementing these rules exist. The authors have compared these rules to a selection rule based on sample variances, and limited study suggest that, when n is large, the difference between the rules based on BAN estimates and the variance rule, in terms of the expected proportion of the selected subset, is minimal. Moreover, since the exact distribution theory for BAN estimates is too complicated, and these BAN estimates are much harder to compute than the sample variances, the selection rule based on the sample variances may be preferred. (Author).

Author: S. Jeyaratnam
Publisher:
ISBN:
Category :
Languages : en
Pages : 26

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Let p sub 1, p sub 2, ..., pi sub k be k independent normal populations with unknown means theta sub 1, theta sub 2, ..., theta sub k, respectively, and a common known variance tau sub 2. The population associated with the largest theta sub i is called the best population. In the subset selection approach, the authors want to select a nonempty subset of the k populations so that it includes the best population with a minimum guaranteed probability. The basic idea of the subset selection approach is that the number of populations to be selected should depend upon the evidence supplied by the data.

Author: Shanti Swarup Gupta
Publisher:
ISBN:
Category :
Languages : en
Pages : 24

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This paper deals with the classical Gupta (1956,65)-approach (Minimize the expected subset size under the P*-condition) in the case of three normal populations with a common known variance and equal sample sizes n. By the method of Lagrangian (undetermined) multipliers a function (involving psi and phi-terms only) is derived which is a convenient tool to find optimal procedures within Seal's (1955,57) class. Numerical work together with asymptotical results lead to the conclusion that for every fixed P* and mean vector mu, Gupta's (1956) means procedure is optimal within Seal's class for sufficiently large sample size n. (Author).