Asymptotic properties of the MLE in distributional regression under random censoring

Statistics & Probability Letters, vol. 237, pp. 110827

Abstract

Distributional regression aims to find the best candidate in a given parametric family of conditional distributions to model a given dataset. As each candidate in the distribution family can be identified by the corresponding distribution parameters, a common approach for this task is to use the maximum likelihood estimator (MLE) for the parameters. In this paper, we establish theoretical results for this estimator in case the response variable is subject to random right censoring. In particular, we provide proofs of almost sure consistency and asymptotic normality of the MLE under censoring. The empirical behavior is illustrated by a simulation study and a real data example.

Authors 2

1. Gitte Kremling corresponding Aachen Department of Medical Engineering and Technomathematics

   FH Aachen

   Affiliation as printed

   FH Aachen University of Applied Sciences, Department of Medical Engineering and Technomathematics, Heinrich-Mußmann-Str. 1, Jülich, 52428, Germany

2. Gerhard Dikta Aachen Department of Medical Engineering and Technomathematics

   FH Aachen

   Affiliation as printed

   FH Aachen University of Applied Sciences, Department of Medical Engineering and Technomathematics, Heinrich-Mußmann-Str. 1, Jülich, 52428, Germany