Goodness-of-fit tests for the error distribution in nonparametric regression

Suppose the random vector (X, Y) satisfies the regression model Y = m(X)+σ(X)ε, where m(·) = E(Y|·), σ2 (·) = Var(Y |·) and ε is independent of X . The covariate X is d-dimensional (d ≥ 1), the response Y is one-dimensional, and m and σ are unknown but smooth functions. In this paper we study goodness-of-fit tests for the parametric form of the error distribution under this model, without assuming any parametric form for m or σ. The proposed tests are based on the difference between a nonparametric estimator of the error distribution and an estimator obtained under the null hypothesis of a parametric model. The large sample properties of the proposed test statistics are obtained, as well as those of the estimator of the parameter vector under the null hypothesis. Finally, the finite sample behavior of the proposed statistics, and the selection of the bandwidths for estimating m and σ are extensively studied via simulations.

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Document type	Document de travail (Working Paper)
Access type	Accès libre
Publication date	2009
Language	Anglais
Number of pages	18 pages
Collection	STAT Discussion Paper - 0912
Affiliation	UCL - EUEN/STAT - Institut de statistique
Keywords	Bandwidth selection ; bootstrap ; error distribution ; goodness-of-fit tests ; least squares estimation ; local polynomial estimation ; maximum likelihood ; nonparametric regression
Links	http://sites.uclouvain.be/IAP-Stat-Phase-V-VI/ISBApub/ISBAdp.html#2009 http://hdl.handle.net/2078.1/116691[Handle]

See also
	[boreal:34700]	Goodness-of-fit tests for the error distribution in nonparametric regression