Nonparametric regression with filtered data

TL;DR

This paper introduces a flexible nonparametric regression estimation method that handles various data filtering scenarios, including truncation and censoring, by estimating hazard or survivor functions and integrating, with improvements for structured models and asymptotic properties.

Contribution

It proposes a novel nonparametric regression approach accommodating complex data filtering, extending existing methods to both mean and median regression with theoretical guarantees.

Findings

Method effectively handles left truncation and right censoring.

Improved performance when model structure assumptions are valid.

Establishes asymptotic normality of estimators.

Abstract

We present a general principle for estimating a regression function nonparametrically, allowing for a wide variety of data filtering, for example, repeated left truncation and right censoring. Both the mean and the median regression cases are considered. The method works by first estimating the conditional hazard function or conditional survivor function and then integrating. We also investigate improved methods that take account of model structure such as independent errors and show that such methods can improve performance when the model structure is true. We establish the pointwise asymptotic normality of our estimators.