arXiv subjects

Gerhard Dikta

Publications and source records attributed to Gerhard Dikta.

2 recordsLinked to original sources

arXiv2025

Asymptotic properties of the MLE in distributional regression under random censoring

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.

math.ST↗

arXiv2024

Bootstrap-Based Goodness-of-Fit Test for Parametric Families of Conditional Distributions

A consistent goodness-of-fit test for distributional regression is introduced. The test statistic is based on a process that traces the difference between a nonparametric and a semi-parametric estimate of the marginal distribution function of Y. As its asymptotic null distribution is not distribution-free, a parametric bootstrap method is used to determine critical values. Empirical results suggest that, in certain scenarios, the test outperforms existing specification tests by achieving a higher power and thereby offering greater sensitivity to deviations from the assumed parametric distribution family. Notably, the proposed test does not involve any hyperparameters and can easily be applied to individual datasets using the gofreg-package in R.

stat.ME↗