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Goodness-of-fit tests in parametric regression based on the estimation of the error distribution

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Van Keilegom, Ingrid [UCL] Manteiga, Wenceslao Gonzalez Sellero, Cesar Sanchez

Consider a heteroscedastic regression model Y = m(X) + s(X) e, where m(X) = E(Y vertical bar X) and sigma(2)(X) = Var(Y vertical bar X) are unknown, and the error e is independent of the covariate X. We propose a new type of test statistic for testing whether the regression curve m(.) belongs to some parametric family of regression functions. The proposed test statistic measures the distance between the empirical distribution function of the parametric and of the nonparametric residuals. The asymptotic theory of the proposed test is developed, and the proposed testing procedure is illustrated by means of a small simulation study and the analysis of a data set.

Document type Article de périodique (Journal article) – Article de recherche
Access type Accès restreint
Publication date 2008
Language Anglais
Journal information "Test" - Vol. 17, no. 2, p. 401-415 (2008)
Peer reviewed yes
Publisher Springer (New York)
issn 1133-0686
e-issn 1863-8260
Publication status Publié
Affiliation UCL - EUEN/STAT - Institut de statistique
Keywords bootstrap ; goodness-of-fit ; heteroscedastic regression ; model check ; nonlinear regression ; nonparametric regression ; residual distribution
Links
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Bibliographic reference Van Keilegom, Ingrid ; Manteiga, Wenceslao Gonzalez ; Sellero, Cesar Sanchez. Goodness-of-fit tests in parametric regression based on the estimation of the error distribution. In: Test, Vol. 17, no. 2, p. 401-415 (2008)
Permanent URL http://hdl.handle.net/2078.1/36402