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expected subset size risk; largest location parameter; Gupta-type rule; $L$-estimates; linear combinations of order statistics; monotone likelihood ratio; minimax; asymptotic normality

References:

[1] R. E. Balow S. S. Gupta: **Selection procedures for restricted families of probability distributions**. Ann. Math. Statist. 40 (1969), 905 - 917. DOI 10.1214/aoms/1177697596 | MR 0240912

[2] N. S. Bartlett Z. Govindarajulu: **Some distribution-free statistics and their application to the selection problem**. Ann. Inst. Statist. Math. 20 (1968), 79-97. DOI 10.1007/BF02911626 | MR 0226801

[3] R. E. Bechhofer: **A single-sample multiple decision procedure for ranking means of normal populations with known variances**. Ann. Math. Statist. 25 (1954), 16-39. DOI 10.1214/aoms/1177728845 | MR 0060197 | Zbl 0055.13003

[4] R. L. Berger: **Minimax subset selection for loss measured by subset size**. Ann. Statist. 7 (1979), 1333-1338. DOI 10.1214/aos/1176344851 | MR 0550155 | Zbl 0418.62022

[5] R. J. Carrol S. S. Gupta: **On the probabilities of rankings of k populations**. J. Statist. Comput. Simul. 5 (1977), 145-157. DOI 10.1080/00949657708810147 | MR 0464477

[6] R. N. Curnow C. W. Dunnet: **The numerical evaluation of certain multivariate normal integrals**. Ann. Math. Statist. 33 (1962), 571 - 579. DOI 10.1214/aoms/1177704581 | MR 0137234

[7] S. S. Gupta: **On some multiple decision (selection and ranking) rules**. Technometrics 7 (1965), 225-245. DOI 10.1080/00401706.1965.10490251 | Zbl 0147.17902

[8] S. S. Gupta A. K. Singh: **On rules based on sample medians for selection of the largest location parameter**. Commun. Statist. - Theor. Meth. A 9 (1980), 1277-1298. DOI 10.1080/03610928008827958 | MR 0578557

[9] J. Hustý: **Ranking and selection procedures for location parameter case based on L-estimates**. Apl. mat. 26 (1981), 377-388. MR 0631755

[10] J. Hustý: **Total positivity of the density of a linear combination of order statistics**. To appear in Čas. pěst. mat.

[11] T. J. Santner: **A restricted subset selection approach to ranking and selection problems**. Ann. Statist. 3 (1975), 334-349. DOI 10.1214/aos/1176343060 | MR 0370884 | Zbl 0302.62011

[12] P. K. Sen: **An invariance principle for linear combinations of order statistics**. Z. Wahrscheinlichkeitstheorie verw. Gebiete 42 (1978), 327-340. DOI 10.1007/BF00533468 | MR 0483171 | Zbl 0362.60022

[13] S. M. Stigler: **Linear functions of order statistics with smooth weight functions**. Ann. Statist. 2 (1974), 676-693. DOI 10.1214/aos/1176342756 | MR 0373152 | Zbl 0286.62028