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    Please use this identifier to cite or link to this item: https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/20652

    Title: A revisit to the common mean problem: Comparing the maximum likelihood estimator with the Graybill–Deal estimator
    Authors: Pal, Nabendu;Lin, Jyh-jiuan;Chang, Ching-hui;Somesh, Kumar
    Contributors: 淡江大學統計學系
    Keywords: Admissibility;Inadmissibility;Asymptotic variance
    Date: 2007-08-15
    Issue Date: 2009-11-30 12:55:02 (UTC+8)
    Publisher: Amsterdam: Elsevier BV
    Abstract: For estimating the common mean of two normal populations with unknown and possibly unequal variances the well-known Graybill–Deal estimator (GDE) has been a motivating factor for research over the last five decades. Surprisingly the literature does not have much to show when it comes to the maximum likelihood estimator (MLE) and its properties compared to those of the GDE. The purpose of this note is to shed some light on the structure of the MLE, and compare it with the GDE. While studying the asymptotic variance of the GDE, we provide an upgraded set of bounds for its variance. A massive simulation study has been carried out with very high level of accuracy to compare the variances of the above two estimators results of which are quite interesting.
    Relation: Computational Statistics and Data Analysis 51(12), pp.5673-5681
    DOI: 10.1016/j.csda.2007.04.004
    Appears in Collections:[Graduate Institute & Department of Statistics] Journal Article

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