Asymptotic normality of H-L estimators based on dependent data |
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Authors: | Hira Lal Koul |
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Institution: | 1. Michigan State University, Michigan, USA
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Abstract: | LetX 1,X 2, ... be a strictly stationary φ-mixing sequence of r.v.'s with a common continuous cdfF. Let θ be a location parameter ofF. We prove the asymptotic normality of a class of Hodges-Lehmann estimators of θ under various regularity conditions on the mixing number φ and the underlyingF. We also establish the asymptotic linearity of signed rank statistics in the parameter θ. Our results also enable us to study the effect of φ-dependence on the asymptotic power of signed rank tests for testingH 0: θ=0 againstH n :θ=θ 0 n ?1/2,θ 0≠0. Finally these results are shown to remain valid for strongly mixing processes {X i } also. |
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