Partitioning-estimates of a regression function under random censoring

A. Carbonez, L. Györfi, Edward C. van der Meulen

Research output: Contribution to journalArticle

37 Citations (Scopus)

Abstract

Let X be a random vector taking values in IRd and let Y be a non-negative bounded random variable. Moreover, assume a right censoring random variable C, with continuous distribution function, operating on Y, independently of X and Y. In this randomly censored situation, we want to estimate Y based on the vector X of covariates, so that the mean squared error is minimized. For this purpose we construct a nonparametric partitioning estimate mn(z), which is a histogram-like mean regression function estimate, and prove its strong consistency under no smoothness condition on the regression function or on the distribution of X, in the sense that the integrated squared error between the estimate and the regression function tends to zero almost surely as the sample size n tends to infinity.

Original languageEnglish
Pages (from-to)21-38
Number of pages18
JournalStatistics and Risk Modeling
Volume13
Issue number1
DOIs
Publication statusPublished - Jan 1995

Keywords

  • a.s. consistency
  • excess error
  • mean regression function
  • partitioning estimate
  • random censoring

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Statistics, Probability and Uncertainty

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