Efficient quantile regression under censoring using Laguerre polynomials

doi:10.3150/24-BEJ1829

2025-11-01

PRE

Alexander Kreiß *

Ingrid Van Keilegom

DOI：10.3150/24-BEJ1829

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摘要

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In this paper, we consider a novel methodology to estimate linear quantile regression models when the response is randomly right censored. The proposed methodology is based on approximating the error distribution by means of an extension of the Laplace distribution, that is flexible enough to approximate any continuous distribution as long as the number of parameters in this Enriched Laplace distribution grows to infinity. The extension is obtained by enriching the Laplace density by means of Laguerre polynomials in such a way that the new density has by construction the property that its quantile of interest is equal to zero. Hence, when the error term has an Enriched Laplace density, it satisfies by construction the constraints of a quantile regression model. We will show that, with this new quantile regression model, we can obtain novel estimators of the quantile function, which are shown to be consistent and asymptotically normal. We also establish the asymptotic efficiency bound, and show by means of a simulation study and the analysis of data on Covid-19 patients that the proposed method works well in practice compared to competing estimators.

Keyword:

Censored data

Laguerre polynomials

quantile regression

semi-parametric regression