Non-parametric Regression with Dependent Censored Data
Let (<b>"X"</b><sub><b>"i"</b></sub>,<b>"Y"</b><sub><b>"i"</b></sub>) (<b>"i"</b>=<b>"1"</b>,…,<b>"n"</b>) be "n" replications of a random vector (<b>"X"</b>,<b>"Y"</b> ), where "Y" is supposed to be subject to random right censoring. The data (<b>"X"</b><sub><b>"i"</b></sub>,<b>"Y"</b><sub><b>"i"</b></sub>) are assumed to come from a stationary "&agr;"-mixing process. We consider the problem of estimating the function "m"("x") =<scriptface>E</scriptface>("φ"(<b>"Y"</b>)&thi nsp;| <b>"X"</b>=<b>"x"</b>), for some known transformation "φ". This problem is approached in the following way: first, we introduce a transformed variable <formula format="inline"><file name="sjos_586_mu1.gif" type="gif" /></formula>, that is not subject to censoring and satisfies the relation <formula format="inline"><file name="sjos_586_mu2.gif" type="gif" /></formula>, and then we estimate <b>"m"</b>(<b>"x"</b>) 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. Copyright (c) Board of the Foundation of the Scandinavian Journal of Statistics 2008.
