A note on Pitman's measure of closeness with balanced loss function |
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Authors: | Mohammad Jafari Jozani |
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Affiliation: | 1. Department of Statistics, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2m_Jafari_Jozani@umanitoba.ca |
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Abstract: | In this note, we consider the problem of estimating an unknown parameter θ in the sense of the Pitman's measure of closeness (PMC) using the balanced loss function (BLF). We show that the PMC comparison of estimators under the BLF can be reduced to the PMC comparison under the usual absolute error loss. The Pitman-closest estimators of the location and scale parameters under BLF are also characterized. Illustrative examples are given to show the broad range applications of the obtained results. |
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Keywords: | balanced loss function equivariant estimator median-unbiasedness Pitman closeness |
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