Sankhya: The Indian Journal of Statistics

1994, Volume 56, Series B, Pt. 2 , pp. 193--206

ON RESTRICTED SUBSET SELECTION RULES FOR SELECTING THE BEST POPULATION

By

SHANTI S. GUPTA, Purdue University

and

TACHEN LIANG, Wayne State University

SUMMARY. This paper deals with the problem of selecting the best from among k ( 2) location parameter models having c.d.f.G(x- q i ). i =1,k, respectively. A population p i is said to be the best if $\theta_{i}=max_{1\leq j \leq k} \theta_j$. For a specified positive constant d * , a population p i is said to be good if $max_{1\leq j \leq k} (\theta_j-\theta_i) \leq \delta^*$ and bad otherwise. We assume that there is no prior information about the possible configurations of the parameters q 1, , q k. Our goal is to select a subset so that the best population is included in the selected subset and only a good populations are selected. A selection procedure achieving the P*-condition for the general location-parameter-models is proposed. We then specialize it for normal distribution models N(q i, s 2). Some modified selection rules are also investigated. These modified selection rules will achieve the P*-condition as well as control the expected value of the number of the bad populations selected. Finally, an example is presented is to illustrate the implementation of the selection rules.

AMS (1980) subject classification. 62F07.

Key words and phrases. Best population, $P^*$-condition, selection goal, subset selection, correct selection, two-stage selection rule, location-parameter.

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This article in mathematical reviews.