Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: Jul, 1987, Volume 55, Issue 4

Asymptotically Efficient Estimation in the Presence of Heteroskedasticity of Unknown Form<875:AEEITP>2.0.CO;2-A
p. 875-891

P. M. Robinson

In a multiple regression model the residual variance is an unknown function of the explanatory variables, and estimated by nearest neighbor nonparametric regression. The resulting weighted least squares estimator of the regression coefficients is shown to be adaptive, in the sense of having the same asymptotic distribution, to first order, as estimators based on knowledge of the actual variance function or a finite parameterization of it. A similar result was established by Carroll (1982) using kernel estimation and under substantially more restrictive conditions on the data generating process than ours. Extensions to various other models seem to be possible.

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