| Title:
|
Subset selection of the largest location parameter based on $L$-estimates (English) |
| Author:
|
Hustý, Jaroslav |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
29 |
| Issue:
|
6 |
| Year:
|
1984 |
| Pages:
|
397-410 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
expected subset size risk |
| Keyword:
|
largest location parameter |
| Keyword:
|
Gupta-type rule |
| Keyword:
|
$L$-estimates |
| Keyword:
|
linear combinations of order statistics |
| Keyword:
|
monotone likelihood ratio |
| Keyword:
|
minimax |
| Keyword:
|
asymptotic normality |
| MSC:
|
62C99 |
| MSC:
|
62F07 |
| MSC:
|
62F35 |
| MSC:
|
62G30 |
| idZBL:
|
Zbl 0566.62019 |
| idMR:
|
MR0767493 |
| DOI:
|
10.21136/AM.1984.104114 |
| . |
| Date available:
|
2008-05-20T18:26:08Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104114 |
| . |
| Reference:
|
[1] R. E. Balow S. S. Gupta: Selection procedures for restricted families of probability distributions.Ann. Math. Statist. 40 (1969), 905 - 917. MR 0240912, 10.1214/aoms/1177697596 |
| Reference:
|
[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. MR 0226801, 10.1007/BF02911626 |
| Reference:
|
[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. Zbl 0055.13003, MR 0060197, 10.1214/aoms/1177728845 |
| Reference:
|
[4] R. L. Berger: Minimax subset selection for loss measured by subset size.Ann. Statist. 7 (1979), 1333-1338. Zbl 0418.62022, MR 0550155, 10.1214/aos/1176344851 |
| Reference:
|
[5] R. J. Carrol S. S. Gupta: On the probabilities of rankings of k populations.J. Statist. Comput. Simul. 5 (1977), 145-157. MR 0464477, 10.1080/00949657708810147 |
| Reference:
|
[6] R. N. Curnow C. W. Dunnet: The numerical evaluation of certain multivariate normal integrals.Ann. Math. Statist. 33 (1962), 571 - 579. MR 0137234, 10.1214/aoms/1177704581 |
| Reference:
|
[7] S. S. Gupta: On some multiple decision (selection and ranking) rules.Technometrics 7 (1965), 225-245. Zbl 0147.17902, 10.1080/00401706.1965.10490251 |
| Reference:
|
[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. MR 0578557, 10.1080/03610928008827958 |
| Reference:
|
[9] J. Hustý: Ranking and selection procedures for location parameter case based on L-estimates.Apl. mat. 26 (1981), 377-388. MR 0631755 |
| Reference:
|
[10] J. Hustý: Total positivity of the density of a linear combination of order statistics.To appear in Čas. pěst. mat. |
| Reference:
|
[11] T. J. Santner: A restricted subset selection approach to ranking and selection problems.Ann. Statist. 3 (1975), 334-349. Zbl 0302.62011, MR 0370884, 10.1214/aos/1176343060 |
| Reference:
|
[12] P. K. Sen: An invariance principle for linear combinations of order statistics.Z. Wahrscheinlichkeitstheorie verw. Gebiete 42 (1978), 327-340. Zbl 0362.60022, MR 0483171, 10.1007/BF00533468 |
| Reference:
|
[13] S. M. Stigler: Linear functions of order statistics with smooth weight functions.Ann. Statist. 2 (1974), 676-693. Zbl 0286.62028, MR 0373152, 10.1214/aos/1176342756 |
| . |
