Information inequalities for the minimax risk of sequential estimators (with applications)

Lesław Gajek; B. Mizera-Florczak

Applicationes Mathematicae (1998)

  • Volume: 25, Issue: 1, page 85-100
  • ISSN: 1233-7234

Abstract

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Information inequalities for the minimax risk of sequential estimators are derived in the case where the loss is measured by the squared error of estimation plus a linear functional of the number of observations. The results are applied to construct minimax sequential estimators of: the failure rate in an exponential model with censored data, the expected proportion of uncensored observations in the proportional hazards model, the odds ratio in a binomial distribution and the expectation of exponential type random variables.

How to cite

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Gajek, Lesław, and Mizera-Florczak, B.. "Information inequalities for the minimax risk of sequential estimators (with applications)." Applicationes Mathematicae 25.1 (1998): 85-100. <http://eudml.org/doc/219196>.

@article{Gajek1998,
abstract = {Information inequalities for the minimax risk of sequential estimators are derived in the case where the loss is measured by the squared error of estimation plus a linear functional of the number of observations. The results are applied to construct minimax sequential estimators of: the failure rate in an exponential model with censored data, the expected proportion of uncensored observations in the proportional hazards model, the odds ratio in a binomial distribution and the expectation of exponential type random variables.},
author = {Gajek, Lesław, Mizera-Florczak, B.},
journal = {Applicationes Mathematicae},
keywords = {odds ratio; information inequalities; censored data; minimax estimation; proportional hazard model; proportional hazards model},
language = {eng},
number = {1},
pages = {85-100},
title = {Information inequalities for the minimax risk of sequential estimators (with applications)},
url = {http://eudml.org/doc/219196},
volume = {25},
year = {1998},
}

TY - JOUR
AU - Gajek, Lesław
AU - Mizera-Florczak, B.
TI - Information inequalities for the minimax risk of sequential estimators (with applications)
JO - Applicationes Mathematicae
PY - 1998
VL - 25
IS - 1
SP - 85
EP - 100
AB - Information inequalities for the minimax risk of sequential estimators are derived in the case where the loss is measured by the squared error of estimation plus a linear functional of the number of observations. The results are applied to construct minimax sequential estimators of: the failure rate in an exponential model with censored data, the expected proportion of uncensored observations in the proportional hazards model, the odds ratio in a binomial distribution and the expectation of exponential type random variables.
LA - eng
KW - odds ratio; information inequalities; censored data; minimax estimation; proportional hazard model; proportional hazards model
UR - http://eudml.org/doc/219196
ER -

References

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  13. R. Magiera (1977), On sequential minimax estimation for the exponential class of processes, Zastos. Mat. 15, 445-454. Zbl0371.62115
  14. B. Mizera (1996), Lower bounds on the minimax risk of sequential estimators, Statistics 28, 123-129. Zbl0864.62055
  15. W. Rudin (1976), Principles of Mathematical Analysis, McGraw-Hill, New York. Zbl0346.26002
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