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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Koul, H.L. Asymptotic normality of H-L estimators based on dependent data. Ann Inst Stat Math 27, 429–441 (1975). https://doi.org/10.1007/BF02504661
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DOI: https://doi.org/10.1007/BF02504661