Recursive estimates of quantile based on 0-1 observations

Pavel Charamza

Applications of Mathematics (1992)

  • Volume: 37, Issue: 3, page 173-192
  • ISSN: 0862-7940

Abstract

top
The objective of this paper is to introduce some recursive methods that can be used for estimating an L D - 50 value. These methods can be used more generally for the estimation of the γ -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.

How to cite

top

Charamza, Pavel. "Recursive estimates of quantile based on 0-1 observations." Applications of Mathematics 37.3 (1992): 173-192. <http://eudml.org/doc/15709>.

@article{Charamza1992,
abstract = {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.},
author = {Charamza, Pavel},
journal = {Applications of Mathematics},
keywords = {nonparametric methods; isotonic regression; quantile; recursive methods; $LD-50$ value; 0-1 observations; Robbins-Monro procedure; examples; stochastic approximation; nonparametric methods; isotonic regression; quantile; recursive methods; -50 value; 0-1 observations; Robbins-Monro procedure; examples},
language = {eng},
number = {3},
pages = {173-192},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Recursive estimates of quantile based on 0-1 observations},
url = {http://eudml.org/doc/15709},
volume = {37},
year = {1992},
}

TY - JOUR
AU - Charamza, Pavel
TI - Recursive estimates of quantile based on 0-1 observations
JO - Applications of Mathematics
PY - 1992
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 37
IS - 3
SP - 173
EP - 192
AB - 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.
LA - eng
KW - nonparametric methods; isotonic regression; quantile; recursive methods; $LD-50$ value; 0-1 observations; Robbins-Monro procedure; examples; stochastic approximation; nonparametric methods; isotonic regression; quantile; recursive methods; -50 value; 0-1 observations; Robbins-Monro procedure; examples
UR - http://eudml.org/doc/15709
ER -

References

top
  1. Barlow R. E., Bartholomew D. J., Bremner J. M., and Brunk H.D., Statistical Inference Under Order Restrictions, Wiley, London, 1972. (1972) 
  2. Blum J. R., Multidimensional stochastic approximation procedures, AMS 25 (1954), 737-744. (1954) MR0065092
  3. Charamza P., Stochastic approximation on the lattice, Diploma work, Faculty of mathematics and physics, Charles University Prague, 1984. (In Czech.) (1984) 
  4. Charamza P., Software for stochastic approximation, Proceedings of the conference ROBUST 1990. (1990) 
  5. Derman C., Non-parametric up-and-down experimentation, AMS 28 (1957), 795-797. (1957) Zbl0084.14801MR0090956
  6. Dixon Mood, 10.1080/01621459.1948.10483254, JASA 43 (1948), 109-126. (1948) DOI10.1080/01621459.1948.10483254
  7. Dupač V., 10.1007/BF02613138, Metrika 34 (1987), 117-123. (1987) MR0882505DOI10.1007/BF02613138
  8. Dupač V., Henkenrath U., On integer stochastic approximation, Aplikace matematiky 29 (1984), 372-383. (1984) MR0772272
  9. Fabián V., On asymptotic normality in stochastic approximation, AMS 39 (1968), 1327-1332. (1968) MR0231429
  10. Holst U., Recursive estimation of quantiles, Contributions to probability and statistics in honor of Gunnar Blom, Univ. Lund, 1985, pp. 179-188. (1985) Zbl0575.62074MR0795057
  11. Lord P. M., 10.1080/01621459.1971.10482333, Journal of the American Statistical Association 66 (1971), 707-711. (1971) Zbl0257.62049DOI10.1080/01621459.1971.10482333
  12. Mukerjee H. G., A stochastic approximation by observation on a discrete lattice using isotonic regression, AMS 9 (1981), 1020-1025. (1981) MR0628757
  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. (1975) MR0395113
  14. Robbins H., Lai T. L., Adaptive design and stochastic approximation, AS 7 (1979), 1196-1221. (1979) Zbl0426.62059MR0550144
  15. Robbins H., Lai T. L., 10.1007/BF00536178, Z. Wahrsch. Verw. Gebiete 56 (1981), 329-360. (1981) Zbl0472.62089MR0621117DOI10.1007/BF00536178
  16. Roth, Josífko, Malý, Trčka, Statistical methods in experimental medicine, Státní. zdravotnické nakladatelství, Praha, 1962, pp. 592. (In Czech.) (1962) 
  17. Sacks J., Asymptotic distribution of stochastic approximation procedures, AMS 29 (1958), 373-405. (1958) Zbl0229.62010MR0098427
  18. Wu C.F. J., 10.1080/01621459.1985.10478213, Journal of the American Statistical Association 80 (1985), 974-984. (1985) Zbl0588.62133MR0819603DOI10.1080/01621459.1985.10478213
  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. (1981) MR0637943

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.