# Subset selection of the largest location parameter based on $L$-estimates

Aplikace matematiky (1984)

• Volume: 29, Issue: 6, page 397-410
• ISSN: 0862-7940

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## Abstract

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The problem of selecting a subset of polulations containing the population with the largest location parameter is considered. As a generalization of selection rules based on sample means and on sample medians, a rule based on $L$-estimates of location is proposed. This rule is strongly monotone and minimax, the risk being the expected subset size, provided the underlying density has monotone likelihood ratio. The problem of fulfilling the $P*$-condition is solved explicitly only asymptotically, under the asymptotic normality of the $L$-estimates used. However, after replacing their asymptotic variance by its estimate, the solution becomes distribution free.

## How to cite

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Hustý, Jaroslav. "Subset selection of the largest location parameter based on $L$-estimates." Aplikace matematiky 29.6 (1984): 397-410. <http://eudml.org/doc/15374>.

@article{Hustý1984,
abstract = {The problem of selecting a subset of polulations containing the population with the largest location parameter is considered. As a generalization of selection rules based on sample means and on sample medians, a rule based on $L$-estimates of location is proposed. This rule is strongly monotone and minimax, the risk being the expected subset size, provided the underlying density has monotone likelihood ratio. The problem of fulfilling the $P*$-condition is solved explicitly only asymptotically, under the asymptotic normality of the $L$-estimates used. However, after replacing their asymptotic variance by its estimate, the solution becomes distribution free.},
author = {Hustý, Jaroslav},
journal = {Aplikace matematiky},
keywords = {expected subset size risk; largest location parameter; Gupta-type rule; $L$-estimates; linear combinations of order statistics; monotone likelihood ratio; minimax; asymptotic normality; expected subset size risk; largest location parameter; Gupta-type rule; L-estimates; linear combinations of order statistics; monotone likelihood ratio; minimax; asymptotic normality},
language = {eng},
number = {6},
pages = {397-410},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Subset selection of the largest location parameter based on $L$-estimates},
url = {http://eudml.org/doc/15374},
volume = {29},
year = {1984},
}

TY - JOUR
AU - Hustý, Jaroslav
TI - Subset selection of the largest location parameter based on $L$-estimates
JO - Aplikace matematiky
PY - 1984
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 29
IS - 6
SP - 397
EP - 410
AB - The problem of selecting a subset of polulations containing the population with the largest location parameter is considered. As a generalization of selection rules based on sample means and on sample medians, a rule based on $L$-estimates of location is proposed. This rule is strongly monotone and minimax, the risk being the expected subset size, provided the underlying density has monotone likelihood ratio. The problem of fulfilling the $P*$-condition is solved explicitly only asymptotically, under the asymptotic normality of the $L$-estimates used. However, after replacing their asymptotic variance by its estimate, the solution becomes distribution free.
LA - eng
KW - expected subset size risk; largest location parameter; Gupta-type rule; $L$-estimates; linear combinations of order statistics; monotone likelihood ratio; minimax; asymptotic normality; expected subset size risk; largest location parameter; Gupta-type rule; L-estimates; linear combinations of order statistics; monotone likelihood ratio; minimax; asymptotic normality
UR - http://eudml.org/doc/15374
ER -

## References

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8. S. S. Gupta A. K. Singh, 10.1080/03610928008827958, Commun. Statist. - Theor. Meth. A 9 (1980), 1277-1298. (1980) MR0578557DOI10.1080/03610928008827958
9. J. Hustý, Ranking and selection procedures for location parameter case based on L-estimates, Apl. mat. 26 (1981), 377-388. (1981) MR0631755
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, 10.1214/aos/1176343060, Ann. Statist. 3 (1975), 334-349. (1975) Zbl0302.62011MR0370884DOI10.1214/aos/1176343060
12. P. K. Sen, 10.1007/BF00533468, Z. Wahrscheinlichkeitstheorie verw. Gebiete 42 (1978), 327-340. (1978) Zbl0362.60022MR0483171DOI10.1007/BF00533468
13. S. M. Stigler, 10.1214/aos/1176342756, Ann. Statist. 2 (1974), 676-693. (1974) Zbl0286.62028MR0373152DOI10.1214/aos/1176342756

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