Minimum risk equivariant estimator in linear regression model

Jurecková Jana and Picek Jan
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Picek Jan: Technical University in Liberec, Department of Applied Mathematics, CZ-461 17 Liberec 1, Tschechische Republik

Statistics & Risk Modeling, 2009, vol. 27, issue 1, 37-54

Abstract: The minimum risk equivariant estimator (MRE) of the regression parameter vector β in the linear regression model enjoys the finite-sample optimality property, but its calculation is difficult, with an exception of few special cases. We study some possible approximations of MRE, with distribution of the errors being known or unknown: A finite-sample approximation uses the Hájek–Hoeffding projection or the Hoeffding–van Zwet decomposition of an initial equivariant estimator of β, a large-sample approximation is based on the asymptotic representation of the same. A nonparametric approximation uses the expected value with respect to the conditional empirical distribution function, developed by Stute (1986). The only possible approximation avoiding a difficult calculation of conditional expectations is the asymptotic approximation, based on the score function of the underlying distribution of the errors.

Keywords: Asymptotic representation; Hajek-Hoeffding projection; Hoeffding-van Zwet decomposition; linear regression model; maximal invariant (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:bpj:strimo:v:27:y:2009:i:1:p:37-54:n:4

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DOI: 10.1524/stnd.2009.1018

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