# Hoeffding-Type and Bernstein-Type Inequalities for Right Censored Data

## TL;DR

This paper develops Hoeffding-type and Bernstein-type concentration inequalities specifically for right-censored data, providing theoretical bounds and applications in empirical risk minimization.

## Contribution

It introduces new concentration inequalities for IPCW estimators in right-censored data, including standard, data-dependent, uniform, and Bernstein-type bounds.

## Key findings

- Derived Hoeffding-type inequalities for right-censored data
- Established Bernstein-type inequality for IPCW estimators
- Applied inequalities to empirical risk minimization

## Abstract

We present Hoeffding-type and Bernstein-type inequalities for right-censored data. The inequalities bound the difference between an inverse of the probability of censoring weighting (IPCW) estimator and its expectation. We first discuss the asymptotic properties of the estimator and provide conditions for its efficiency. We present standard, data dependent, and uniform Hoeffding-type inequalities. We then present a Bernstein-type inequality. Finally, we show how to apply these inequalities in an empirical risk minimization setting.