Nonparametric regression with cross-sectional data: an alternative to conditional product-limit estimators

English

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 >]

2014

No

[en] Bandwidth selection ; Nonparametric regression ; Survival data ; Cross-sectional data ; Length bias ; Left-truncated and right-censored data

[en] Suppose the random vector (X,Y) satisfies 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 pair (X,Y) is obtained by cross-sectional sampling involving left-truncated and right-censored responses. The considered model is completely nonparametric but the conditional truncation distribution is assumed to be known. The novelty of this work is twofold: first, it extends the results on cross-sectional data to the conditional case and second, it generalizes the length bias results in the conditional case to right censoring and to any truncation distribution. New estimators for m(.) and sigma²(.) are constructed and relevant tools are used to quickly provide the main asymptotic properties for this kind of estimators.
Extensive simulations are carried out and show that the new estimators outperform classical nonparametric estimators for left-truncated and right-censored data (when the truncation model is known). Finally, a data set on the mortality of diabetics is analyzed.

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)