Robust Doubly Protected Estimators for Quantiles with Missing Data

TL;DR

This paper introduces robust doubly protected estimators for quantiles that are resistant to outliers and flexible in modeling the relationship between covariates and responses, addressing missing data issues.

Contribution

It develops robust, semiparametric doubly protected estimators for quantiles with missing data, improving resilience to outliers and model flexibility.

Findings

Estimator robustness to outliers demonstrated

Flexible semiparametric modeling introduced

Effective handling of missing data in quantile estimation

Abstract

Doubly protected estimators are widely used for estimating the population mean of an outcome Y from a sample where the response is missing in some individuals. To compensate for the missing responses, a vector X of covariates is observed at each individual, and the missing mechanism is assumed to be independent of the response, conditioned on X (missing at random). In recent years, many authors have moved from the mean to the median, and more generally, doubly protected estimators of the quantiles have been proposed, assuming a parametric regression model for the relationship between X and Y and a parametric form for the propensity score. In this work, we present doubly protected estimators for the quantiles that are also robust, in the sense that they are resistant to the presence of outliers in the sample. We also flexibilize the model for the relationship between X and Y . Thus we present robust doubly protected estimators for the quantiles of the response in the presence of missing observations, postulating a semiparametric regression model for the relationship between the response and the covariates and a parametric model for the propensity score.