Robust Estimators of Location and Their Second-Order Asymptotic Relations

Jana Jurečková

Chapter Chapter 16 in A Celebration of Statistics, 1985, pp 377-392 from Springer

Abstract: Abstract Let X 1, …, X n be independent random variables, identically distributed according to the distribution function F(x — θ), where θ is the parameter to be estimated. F is generally unspecified; we only assume that F has a symmetric density f. Three broad classes of robust estimators of θ, these of M-estimators, L-estimators, and R-estimators, are first briefly described. Denoting these estimators M n, L n, and R n, respectively, we give sufficient conditions under which these estimators are asymptotically equivalent in probability, i.e., $$\sqrt n (M_n - L_n )\xrightarrow{p}0$$ , etc., as n → ∞. These relations are supplemented by the rates of convergence in most cases.

Keywords: α-trimmed mean; asymptotic equivalence of estimators; Hodges-Lehmann estimator; Huber’s estimator; L-estimator; M-estimator; R-estimator; second-order asymptotic relations of estimators (search for similar items in EconPapers)
Date: 1985
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4613-8560-8_16

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DOI: 10.1007/978-1-4613-8560-8_16

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