Non-parametric Regression with Dependent Censored Data

• Published in: Scandinavian journal of statistics Vol. 35; no. 2; pp. 228 - 247
• Main Authors: GHOUCH, ANOUAR EL, KEILEGOM, INGRID VAN
• Format: Journal Article
• Language: English
• Published: Oxford, UK Blackwell Publishing Ltd 01.06.2008; Blackwell Publishing; Blackwell; Danish Society for Theoretical Statistics
• Series: Scandinavian Journal of Statistics
• Subjects: Censored data; censoring; Censorship; Consistent estimators; Cumulative distribution functions; Data smoothing; Estimators; Exact sciences and technology; General topics; Kaplan Meier estimator; Linear inference, regression; Linear regression; local linear smoothing; Mathematics; Nonparametric inference; Probability and statistics; Probability theory and stochastic processes; Regression analysis; Sciences and techniques of general use; Statistical methods; Statistical theories; Statistical variance; Statistics; Stochastic processes; strong mixing; Studies; survival analysis; Uniform convergence; Mixing; Statistical distribution; Censored sample; Random vector; Kernel estimator; censoring; survival analysis; Distribution function; Convergence rate; Stationary process; Approximation theory; Censored data; Mixed distribution; Convergence acceleration; Mixing process; Linear regression; Kernel estimation; Statistical estimation; Kernel method; Functional; Statistical method; Kernels; Statistical regression; Estimating function; Numerical analysis; local linear smoothing; Application; strong mixing; M estimation
• ISSN: 0303-6898; 1467-9469; 1467-9469
• DOI: 10.1111/j.1467-9469.2007.00586.x

Let (X i , Y ¡ ) (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 ¡ ) are assumed to come from a stationary α-mixing process. We consider the problem of estimating the function m(x) = E(Φ(Y)| X=x), for some known transformation Φ. 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(Φ(Y i ) | X i =x)=E (Y i * | 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.