Density and hazard estimation in censored regression models

Let (X, Y ) be a random vector, where Y denotes the variable of interest, possibly subject to random right censoring, and X is a covariate. Consider a heteroscedastic model Y = m(X) + σ(X)ε, where the error term ε is independent of X and m(X) and σ(X) are smooth but unknown functions. Further, assume that there exists a region of the covariate X where the censoring of Y is light. Under this model, we construct a nonparametric estimator for the density and hazard function of Y given X, which has a faster rate of convergence than the completely nonparametric estimator, that is constructed without making any model assumption. Moreover, the proposed estimator for the density and hazard function performs better in the right tail compared to the classical nonparametric estimator. We prove the weak convergence of both the density and the hazard function estimator. The results are obtained by constructing asymptotic representations for the two estimators and by making use of Van Keilegom and Akritas (1999), where an estimator of the conditional distribution of Y given X is studied under the same model assumption.

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Document type	Document de travail (Working Paper)
Access type	Accès libre
Publication date	2000
Language	Anglais
Number of pages	32 pages
Collection	STAT Discussion Papers - 0036
Affiliations	UCL - EUEN/STAT - Institut de statistique Limburgs universitair Centrum - Department of Mathematics
Keywords	Asymptotic representation ; Density function ; Hazard rate ; Heteroscedas- tic regression ; Right censoring ; Weak convergence
Links	http://sites.uclouvain.be/IAP-Stat-Phase-V-VI/ISBApub/ISBAdp.html#2000 http://hdl.handle.net/2078.1/115104[Handle]

See also
	[boreal:41550]	Density and hazard estimation in censored regression models