Let π1, ... , πk be k independent populations and let Fi ( x)= F( x - θi) be the absolutely continuous cumulative distribution function (cdf) of the i-th population indexed by the location parameter θi; i=1,,.... k. A class of subset selection procedures based on sub-sample extrema for unequal sample sizes is proposed for the problem of selecting a subset from ( π1, .... πk) which contains the population with largest location parameter. The proposed subset selection procedures are then compared with the subset selection procedures of Hsu (1981) in the sense of Pitman ARE (asymptotic relative efficiency). It is shown that these procedures can approximately be implemented with the help of existing tables and sample size sufficient for their implementation, based on simulation results, is discussed. AMS (1980) Subject Classification: Primary 62F07; Secondary 62H10

Chandigarh -160 014 (INDIA). ABSTRACT A new test based on linear combinations of U-statistics for testing homogeneity of location parameters ~gnir~sl, ordered alternatives is proposed. Asymptotic distribution of the test statistic is obtained under the null hypothesis as well as under the sequence of local alternatives. Asymptotic relative efficiencies of this test relative to the existing tests are obtained and it is seen that the proposed test performs batter for heavy-tailed distributions.

Kumar, Mehta, and Kumar (2002) developed two new classes of subset selection procedures for location parameters. In this paper, Pitman asymptotic relative efficiencies are computed for some members of these classes when compared among themselves and to the existing procedures, with interesting results. Approximate implementation of these procedures with the help of existing tables is illustrated. Simulation study is carried out to assess the sample size sufficient for their implementation.

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Summary Let be k independent populations having the same known quantile of order p (0 p 1) and let F(x)=F(x/i) be the absolutely continuous cumulative distribution function of the ith population indexed by the scale parameter 1, i = 1,…, k. We propose subset selection procedures based on two‐sample U‐statistics for selecting a subset of k populations containing the one associated with the smallest scale parameter. These procedures are compared with the subset selection procedures based on two‐sample linear rank statistics given by Gill & Mehta (1989) in the sense of Pitman asymptotic relative efficiency, with interesting results.