Non-parametric regression with dependent censored data
(2008) Scandinavian Journal of Statistics : theory and applications — Vol. 35, n° 2, p. 228-247 (2008)
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- Abstract
- Let (X-i,Y-i) (i=1,...,n) be n replications of a random vector (X,Y ), where Y is supposed to be subject to random right censoring. The data (X-i,Y-i) are assumed to come from a stationary alpha-mixing process. We consider the problem of estimating the function m(x) = E(phi(Y) vertical bar X=x), for some known transformation phi. This problem is approached in the following way: first, we introduce a transformed variable Y-i*, that is not subject to censoring and satisfies the relation E(phi(Y-i) vertical bar X-i = x) = E(phi(Y-i* vertical bar X-i = x)and then we estimate m(x) by applying local linear regression techniques. As a by-product, we obtain a general result on the uniform rate of convergence of kernel type estimators of functionals of an unknown distribution function, under strong mixing assumptions.
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El Ghouch, A., & Van Keilegom, I. (2008). Non-parametric regression with dependent censored data. Scandinavian Journal of Statistics : theory and applications, 35(2), 228-247. https://doi.org/10.1111/j.1467-9469.2007.00586.x (Original work published 2008)