Bandwidth selection; Nonparametric regression; Survival analysis; Cross-sectional data; Left-tru ncated and right-censored data
Abstract :
[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)
Research Center/Unit :
Centre for Quantitative Methods and Operations Management (QuantOM)
Disciplines :
Mathematics
Author, co-author :
Heuchenne, Cédric ; Université de Liège - ULiège > HEC-Ecole de gestion : UER > Statistique appliquée à la gestion et à l'économie
Laurent, Géraldine ; Université de Liège - ULiège > HEC-Ecole de gestion : UER > UER Opérations
Language :
English
Title :
Estimation of the error distribution in nonparametric regression with cross-sectional data
Publication date :
2014
Funders :
This research was supported by IAP research network grant nr. P7/06 of the Belgian government (Belgian Science Policy).
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