Efficient Inference on High-Dimensional Linear Models with Missing Outcomes

TL;DR

This paper introduces a new method for accurate inference in high-dimensional linear models with missing outcomes, combining Lasso estimates with bias correction, and demonstrates its efficiency and robustness through simulations and real data analysis.

Contribution

It proposes a novel estimator that integrates Lasso with a bias correction based on propensity scores, achieving asymptotic normality and efficiency even with machine learning-based propensity score estimation.

Findings

Estimator is asymptotically normal and semi-parametrically efficient.

Maintains properties even when propensity scores are estimated by machine learning.

Validated through simulations and galaxy stellar mass inference.

Abstract

This paper is concerned with inference on the regression function of a high-dimensional linear model when outcomes are missing at random. We propose an estimator which combines a Lasso pilot estimate of the regression function with a bias correction term based on the weighted residuals of the Lasso regression. The weights depend on estimates of the missingness probabilities (propensity scores) and solve a convex optimization program that trades off bias and variance optimally. Provided that the propensity scores can be pointwise consistently estimated at in-sample data points, our proposed estimator for the regression function is asymptotically normal and semi-parametrically efficient among all asymptotically linear estimators. Furthermore, the proposed estimator keeps its asymptotic properties even if the propensity scores are estimated by modern machine learning techniques. We validate the finite-sample performance of the proposed estimator through comparative simulation studies and the real-world problem of inferring the stellar masses of galaxies in the Sloan Digital Sky Survey.