A note on comparison and improvement of estimators based on likelihood |
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Authors: | A. Zaigraev I. Kaniovska |
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Affiliation: | 1. Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Toruń, Poland;2. Institute for Applied System Analysis, NTUU ‘KPI’, Kyiv, Ukraine |
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Abstract: | The problem of estimation of a parameter of interest in the presence of a nuisance parameter, which is either location or scale, is considered. Three estimators are taken into account: usual maximum likelihood (ML) estimator, maximum integrated likelihood estimator and the bias-corrected ML estimator. General results on comparison of these estimators w.r.t. the second-order risk based on the mean-squared error are obtained. Possible improvements of basic estimators via the notion of admissibility and methodology given in Ghosh and Sinha [A necessary and sufficient condition for second order admissibility with applications to Berkson's bioassay problem. Ann Stat. 1981;9(6):1334–1338] are considered. In the recent paper by Tanaka et al. [On improved estimation of a gamma shape parameter. Statistics. 2014; doi:10.1080/02331888.2014.915842], this problem was considered for estimating the shape parameter of gamma distribution. Here, we perform more accurate comparison of estimators for this case as well as for some other cases. |
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Keywords: | maximum likelihood estimator maximum integrated likelihood estimator bias-corrected maximum likelihood estimator mean-squared error second-order risk admissibility |
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