Asymptotic behavior of general M-estimates for regression and scale with random carriers View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1981-03

AUTHORS

Ricardo A. Maronna, Victor J. Yohai

ABSTRACT

Let (xini, yibe a sequence of independent identically distributed random variables, where xi∃Rpand yi∃R, and let θ∃Rpbe an unknown vector such that yi=x′iθ+ui(*), where uiis independent of xiand has distribution function F(u/σ), where σ>0 is an unknown parameter. This paper deals with a general class of M-estimates of regression and scale, (θ*,σ*), defined as solutions of the system:, where r= (yi−xi1θ*/σ)*, with Φ∶ Rp×R→R and χ∶ R→R. This class contains estimators of (θ, σ) proposed by Huber, Mallows and Krasker and Welsch. The consistency and asymptotic normality of the general M-estimators are proved assuming general regularity conditions on Φ and χ and assuming the joint distribution of (xi, yi) to fulfill the model (*) only approximately. More... »

PAGES

7-20

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf00536192

DOI

http://dx.doi.org/10.1007/bf00536192

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1036056545


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