Robust location estimation with missing data

TL;DR

This paper introduces a robust method for estimating the distribution and location parameters of responses with missing data under a semiparametric model, ensuring consistency and robustness against data contamination.

Contribution

It proposes a novel robust estimation approach for distribution and location functionals in missing at random data, with proven consistency and robustness measures.

Findings

Consistent estimation of distribution functionals under MAR data.

Strongly consistent estimates for location functionals like median.

Asymptotic distribution derived for the proposed estimators.

Abstract

In a missing-data setting, we have a sample in which a vector of explanatory variables x_i is observed for every subject i, while scalar outcomes y_i are missing by happenstance on some individuals. In this work we propose robust estimates of the distribution of the responses assuming missing at random (MAR) data, under a semiparametric regression model. Our approach allows the consistent estimation of any weakly continuous functional of the response's distribution. In particular, strongly consistent estimates of any continuous location functional, such as the median or MM functionals, are proposed. A robust fit for the regression model combined with the robust properties of the location functional gives rise to a robust recipe for estimating the location parameter. Robustness is quantified through the breakdown point of the proposed procedure. The asymptotic distribution of the location estimates is also derived.