Reference : Estimation of the error distribution in nonparametric regression with cross-sectional data
E-prints/Working papers : First made available on ORBi
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/2268/168752
Estimation of the error distribution in nonparametric regression with cross-sectional data
English
Heuchenne, Cédric mailto [Université de Liège - ULiège > HEC-Ecole de gestion : UER > Statistique appliquée à la gestion et à l'économie >]
Laurent, Géraldine mailto [Université de Liège - ULiège > HEC-Ecole de gestion : UER > UER Opérations >]
2014
No
[en] Bandwidth selection ; Nonparametric regression ; Survival analysis ; Cross-sectional data ; Left-tru ncated and right-censored data
[en] In this article, we study the nonparametric regression model Y=m(X)+varepsilon where m(x)=E[Y|X=x] and sigma²(x)=Var[varepsilon|X=x] are unknown smooth functions, and the error varepsilon has zero mean and finite variance conditionally on X=x. The problem consists in estimating the cumulative distribution function of the error in a nonparametric way when the couple (X,Y) is obtained by cross-sectional sampling while the positive response Y can be right-censored. We propose a new estimator for the error distribution function based on the estimators of m(.) and sigma²(.) described in Heuchenne and Laurent 2014. A bootstrap procedure is developed to solve the critical problem of the smoothing parameter choice. We assess the performance of the proposed estimator through simulations. Finally, a data set based on the mortality of diabetics is analyzed. (Heuchenne Cédric and Laurent Géraldine, Nonparametric regression with cross-sectional data: an alternative to conditional product-limit estimators, 2014)
Centre for Quantitative Methods and Operations Management (QuantOM)
This research was supported by IAP research network grant nr. P7/06 of the Belgian government (Belgian Science Policy).
http://hdl.handle.net/2268/168752

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