# 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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topHustý, 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 -

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