Regression for partially observed variables and nonparametric quantiles of conditional probabilities

TL;DR

This paper introduces new nonparametric estimators for regression functions and conditional quantiles in models with biased sampling, censoring, or truncation, addressing issues of inconsistency in traditional estimators.

Contribution

It proposes novel nonparametric estimators for regression and quantiles under complex sampling schemes, with discussions on model identifiability.

Findings

New estimators improve consistency under biased sampling

Addresses models with both binary and continuous variables

Provides theoretical insights on model identifiability

Abstract

Efficient estimation under bias sampling, censoring or truncation is a difficult question which has been partially answered and the usual estimators are not always consistent. Several biased designs are considered for models with variables $(X,Y)$ where $Y$ is an indicator and $X$ an explanatory variable, or for continuous variables $(X,Y)$. The identifiability of the models are discussed. New nonparametric estimators of the regression functions and conditional quantiles are proposed.