| Title:
|
Recursive estimates of quantile based on 0-1 observations (English) |
| Author:
|
Charamza, Pavel |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
37 |
| Issue:
|
3 |
| Year:
|
1992 |
| Pages:
|
173-192 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The objective of this paper is to introduce some recursive methods that can be used for estimating an $LD-50$ value. These methods can be used more generally for the estimation of the $\gamma$-quantile of an unknown distribution provided we have 0-1 observations at our disposal. Standard methods based on the Robbins-Monro procedure are introduced together with different approaches of Wu or Mukerjee. Several examples are also mentioned in order to demonstrate the usefulness of the methods presented. (English) |
| Keyword:
|
nonparametric methods |
| Keyword:
|
isotonic regression |
| Keyword:
|
quantile |
| Keyword:
|
recursive methods |
| Keyword:
|
$LD-50$ value |
| Keyword:
|
0-1 observations |
| Keyword:
|
Robbins-Monro procedure |
| Keyword:
|
examples |
| Keyword:
|
stochastic approximation |
| MSC:
|
62G05 |
| MSC:
|
62L20 |
| MSC:
|
62P10 |
| idZBL:
|
Zbl 0764.62068 |
| idMR:
|
MR1157454 |
| DOI:
|
10.21136/AM.1992.104502 |
| . |
| Date available:
|
2008-05-20T18:43:32Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104502 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] Charamza P.: Stochastic approximation on the lattice.Diploma work, Faculty of mathematics and physics, Charles University Prague, 1984. (In Czech.) |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
|
[10] Holst U.: Recursive estimation of quantiles.Contributions to probability and statistics in honor of Gunnar Blom, Univ. Lund, 1985, pp. 179-188. Zbl 0575.62074, MR 0795057 |
| Reference:
|
[11] Lord P. M.: Tailored testing. An application of stochastic approximation.Journal of the American Statistical Association 66 (1971), 707-711. Zbl 0257.62049, 10.1080/01621459.1971.10482333 |
| Reference:
|
[12] Mukerjee H. G.: A stochastic approximation by observation on a discrete lattice using isotonic regression.AMS 9 (1981), 1020-1025. MR 0628757 |
| Reference:
|
[13] Nevelson M. B.: On the properties of the recursive estimates for a functional of an unknown distribution function.Limit Theorems of Probability Theory (P. Revezs, eds.), Amsterodam, 1975, pp. 227-252. MR 0395113 |
| Reference:
|
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| Reference:
|
[15] Robbins H., Lai T. L.: Consistency and asymptotic efficiency of slope estimates in stochastic approximation schemes.Z. Wahrsch. Verw. Gebiete 56 (1981), 329-360. Zbl 0472.62089, MR 0621117, 10.1007/BF00536178 |
| Reference:
|
[16] Roth, Josífko, Malý, Trčka: Statistical methods in experimental medicine.Státní. zdravotnické nakladatelství, Praha, 1962, pp. 592. (In Czech.) |
| Reference:
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[17] Sacks J.: Asymptotic distribution of stochastic approximation procedures.AMS 29 (1958), 373-405. Zbl 0229.62010, MR 0098427 |
| Reference:
|
[18] Wu C.F. J.: Efficient sequential designs with binary data.Journal of the American Statistical Association 80 (1985), 974-984. Zbl 0588.62133, MR 0819603, 10.1080/01621459.1985.10478213 |
| Reference:
|
[19] Silvapulle M. J.: On the existence of maximum likelihood estimators for the binomial response problem.Journal of the Royal Statistical Society, Ser. B 43 (1981), 310-313. MR 0637943 |
| . |
