Density and hazard estimation in censored regression models
(2002) Bernoulli : a journal of mathematical statistics and probability — Vol. 8, n° 5, p. 607-625 (2002)
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- 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) + sigma(X)epsilon, where the error term epsilon is independent of X and m(X) and sigma(C) are smooth but unknown functions. 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 than the classical nonparametric estimator, especially in the right tail of the distribution. 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 work by Van Keilegom and Akritas in which an estimator of the conditional distribution of Y given X is studied under the same model assumption.
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Van Keilegom, I., & Veraverbeke, N. (2002). Density and hazard estimation in censored regression models. Bernoulli : a journal of mathematical statistics and probability, 8(5), 607-625. https://hdl.handle.net/2078.5/33980 (Original work published 2002)