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2019 Generalized M-estimators for high-dimensional Tobit I models
Jelena Bradic, Jiaqi Guo
Electron. J. Statist. 13(1): 582-645 (2019). DOI: 10.1214/18-EJS1463

Abstract

This paper develops robust confidence intervals in high-dimensional and left-censored regression. Type-I censored regression models, where a competing event makes the variable of interest unobservable, are extremely common in practice. In this paper, we develop smoothed estimating equations that are adaptive to censoring level and are more robust to the misspecification of the error distribution. We propose a unified class of robust estimators, including one-step Mallow’s, Schweppe’s, and Hill-Ryan’s estimator that are adaptive to the left-censored observations. 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 estimators inherit asymptotic distribution of fully iterated version. Moreover, we show that the size of the residuals of the Bahadur representation matches those of the pure linear models – that is, the effects of censoring disappear asymptotically. 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.

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Jelena Bradic. Jiaqi Guo. "Generalized M-estimators for high-dimensional Tobit I models." Electron. J. Statist. 13 (1) 582 - 645, 2019. https://doi.org/10.1214/18-EJS1463

Information

Received: 1 May 2017; Published: 2019
First available in Project Euclid: 16 February 2019

zbMATH: 07037999
MathSciNet: MR3914176
Digital Object Identifier: 10.1214/18-EJS1463

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Vol.13 • No. 1 • 2019
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