Robust Confidence Intervals in High-Dimensional Left-Censored Regression

TL;DR

This paper introduces robust, adaptive confidence intervals for high-dimensional left-censored regression, effectively handling censoring and error distribution misspecification, with theoretical guarantees and practical validation.

Contribution

It develops a unified class of robust estimators for censored regression that are adaptive, asymptotically normal, and applicable in ultra-high-dimensional settings.

Findings

Estimator is robust to censoring and error distribution asymmetry.

Asymptotic distribution matches fully observed models under certain conditions.

Method performs well in simulations and real HIV-1 data analysis.

Abstract

This paper develops robust confidence intervals in high-dimensional and left-censored regression. Type-I censored regression models are extremely common in practice, where a competing event makes the variable of interest unobservable. However, techniques developed for entirely observed data do not directly apply to the censored observations. In this paper, we develop smoothed estimating equations that augment the de-biasing method, such that the resulting estimator is adaptive to censoring and is more robust to the misspecification of the error distribution. We propose a unified class of robust estimators, including Mallow's, Schweppe's and Hill-Ryan's one-step estimator. In the ultra-high-dimensional setting, where the dimensionality can grow exponentially with the sample size, we show that as long as the preliminary estimator converges faster than $n^{-1/4}$, the one-step estimator inherits asymptotic distribution of fully iterated version. Moreover, we show that the size of the residuals of the Bahadur representation matches those of the simple linear models, $s^{3/4 } (\log (p \vee n))^{3/4} / n^{1/4}$ -- that is, the effects of censoring asymptotically disappear. Simulation studies demonstrate that our method is adaptive to the censoring level and asymmetry in the error distribution, and does not lose efficiency when the errors are from symmetric distributions. Finally, we apply the developed method to a real data set from the MAQC-II repository that is related to the HIV-1 study.