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

Volume 25 / 1998

Lesław Gajek, B. Mizera-Florczak Applicationes Mathematicae 25 (1998), 85-100 DOI: 10.4064/am-25-1-85-100

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.

Authors

  • Lesław Gajek
  • B. Mizera-Florczak

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