On quantile optimization problem based on information from censored data

Petr Volf

Kybernetika (2018)

  • Volume: 54, Issue: 6, page 1156-1166
  • ISSN: 0023-5954

Abstract

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Stochastic optimization problem is, as a rule, formulated in terms of expected cost function. However, the criterion based on averaging does not take in account possible variability of involved random variables. That is why the criterion considered in the present contribution uses selected quantiles. Moreover, it is assumed that the stochastic characteristics of optimized system are estimated from the data, in a non-parametric setting, and that the data may be randomly right-censored. Therefore, certain theoretical results concerning estimators of distribution function and quantiles under censoring are recalled and then utilized to prove consistency of solution based on estimates. Behavior of solutions for finite data sizes is studied with the aid of randomly generated example of a newsvendor problem.

How to cite

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Volf, Petr. "On quantile optimization problem based on information from censored data." Kybernetika 54.6 (2018): 1156-1166. <http://eudml.org/doc/294789>.

@article{Volf2018,
abstract = {Stochastic optimization problem is, as a rule, formulated in terms of expected cost function. However, the criterion based on averaging does not take in account possible variability of involved random variables. That is why the criterion considered in the present contribution uses selected quantiles. Moreover, it is assumed that the stochastic characteristics of optimized system are estimated from the data, in a non-parametric setting, and that the data may be randomly right-censored. Therefore, certain theoretical results concerning estimators of distribution function and quantiles under censoring are recalled and then utilized to prove consistency of solution based on estimates. Behavior of solutions for finite data sizes is studied with the aid of randomly generated example of a newsvendor problem.},
author = {Volf, Petr},
journal = {Kybernetika},
keywords = {optimization; censored data; product-limit estimator; empirical quantile; newsvendor problem},
language = {eng},
number = {6},
pages = {1156-1166},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On quantile optimization problem based on information from censored data},
url = {http://eudml.org/doc/294789},
volume = {54},
year = {2018},
}

TY - JOUR
AU - Volf, Petr
TI - On quantile optimization problem based on information from censored data
JO - Kybernetika
PY - 2018
PB - Institute of Information Theory and Automation AS CR
VL - 54
IS - 6
SP - 1156
EP - 1166
AB - Stochastic optimization problem is, as a rule, formulated in terms of expected cost function. However, the criterion based on averaging does not take in account possible variability of involved random variables. That is why the criterion considered in the present contribution uses selected quantiles. Moreover, it is assumed that the stochastic characteristics of optimized system are estimated from the data, in a non-parametric setting, and that the data may be randomly right-censored. Therefore, certain theoretical results concerning estimators of distribution function and quantiles under censoring are recalled and then utilized to prove consistency of solution based on estimates. Behavior of solutions for finite data sizes is studied with the aid of randomly generated example of a newsvendor problem.
LA - eng
KW - optimization; censored data; product-limit estimator; empirical quantile; newsvendor problem
UR - http://eudml.org/doc/294789
ER -

References

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  8. Petruzzi, N. C., Dada, M., 10.1287/opre.47.2.183, Oper. Res. 47 (1999), 2, 183-194. DOI10.1287/opre.47.2.183
  9. Rejto, L., On fixed censoring model and consequences for the stochastic case., In: Trans. 9th Prague Conference on Stochastic Decision Functions 1982, Academia, Prague 1983, pp. 141-147. MR0757919
  10. Timofeeva, G. A., 10.1134/s000511790707003x, Automat. Remote Control 68 (2007), 3, 1145-1157. MR2341643DOI10.1134/s000511790707003x
  11. Volf, P., On precision of optimization in the case of incomplete information., Bull. Czech Econometr. Soc. 19 (2012), 170-184. 

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