Second order asymptotic relations of M-estimators and R-estimators in two-sample location model |
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Authors: | Marie Hušková Jana Jurečková |
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Affiliation: | Department of Probability and Statistics, Charles University, Sokolovská 83, 186 00 Prague 8, Czechoslovakia |
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Abstract: | Let TM be an M-estimator (maximum likelihood type estimator) and TR be an R-estimator (Hodges-Lehmann's estimator) of the shift parameter Δ in the two-sample location model. The asymptotic representation of √N(TM-TR) up to a term of the order Op(N-) is derived which is valid if the functions Ψ and ? generating TM and TR, respectively, decompose into an absolutely continuous and a step-function components; the order Op(N-) cannot be improved unless the discontinuous components vanish. As a consequence, the conditions under which √N(TM-TR)=Op(N-) are obtained. The main tool for obtaining the results is the second order asymptotic linearity of the pertaining linear rank statistics which is proved here under the assumption that the score-generating function ? has some jump-discontinuities. |
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Keywords: | 62G05 62F12 60F17 M-Estimator R-Estimator Asymptotic Linearity Invariance Principle |
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