Single index regression models in the presence of censoring depending on the covariates

TL;DR

This paper introduces new estimators for joint distribution and single index regression models with censored data, effectively addressing high-dimensional challenges and providing asymptotic properties.

Contribution

It presents novel estimators for joint distribution and regression parameters under censoring, utilizing a new dimension reduction technique to mitigate the curse of dimensionality.

Findings

New estimator for joint distribution overcomes curse-of-dimensionality

Proposed estimators for single index model parameters are asymptotically consistent

Method effectively handles right-censored data in high-dimensional settings

Abstract

Consider a random vector (X',Y)', where X is d-dimensional and Y is one-dimensional. We assume that Y is subject to random right censoring. The aim of this paper is twofold. First, we propose a new estimator of the joint distribution of (X',Y)'. This estimator overcomes the common curse-of-dimensionality problem, by using a new dimension reduction technique. Second, we assume that the relation between X and Y is given by a mean regression single index model, and propose a new estimator of the parameters in this model. The asymptotic properties of all proposed estimators are obtained.