Density and hazard estimation in censored regression models
(2000) , 32 pages
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- Authors
- Abstract
- 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.
- Affiliations
Limburgs universitair Centrum Department of Mathematics
Citations
Van Keilegom, I., & Veraverbeke, N. (2000). Density and hazard estimation in censored regression models (STAT Discussion Papers 0036). https://hdl.handle.net/2078.5/33203