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Note on unbiased estimability of the larger of two mean values

100%
Gajek L.
Applicationes Mathematicae
|
1995-1996
|
tom 23
|
nr 2
239-245
EN
An unbiased estimator of the larger of two mean values is constructed provided that the number of observations is random.
2
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Information inequalities for the minimax risk of sequential estimators (with applications)

63%
Gajek L., Mizera-Florczak B.
Applicationes Mathematicae
|
1998-1999
|
tom 25
|
nr 1
85-100
EN
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.
3
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On localizing global Pareto solutions in a given convex set

63%
Drwalewska A., Gajek L.
Applicationes Mathematicae
|
1999
|
tom 26
|
nr 4
383-394
EN
Sufficient conditions are given for the global Pareto solution of the multicriterial optimization problem to be in a given convex subset of the domain. In the case of maximizing real valued-functions, the conditions are sufficient and necessary without any convexity type assumptions imposed on the function. In the case of linearly scalarized vector-valued functions the conditions are sufficient and necessary provided that both the function is concave and the scalarization is increasing with respect to the cone generating the preference relation.
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