Parametric modal regression for right-censored positive responses

TL;DR

This paper introduces a parametric modal regression framework for positive continuous data with right-censoring, providing explicit density reparameterizations and demonstrating effectiveness through simulations and real data application.

Contribution

It offers a novel analytical reparameterization linking the mode to the distribution parameters for several positive distributions, enabling efficient censored regression modeling.

Findings

Consistent parameter recovery demonstrated in simulations.

Bias and RMSE decrease with larger samples and less censoring.

Wald confidence intervals achieve nominal coverage.

Abstract

We present a unified parametric framework for modal regression applicable to continuous positive distributions, with explicit support for right-censored observations. The key contribution is a systematic analytical reparameterization of density parameters as direct functions of the conditional mode. This closed-form mapping is derived for the Gamma, Beta, Weibull, Lognormal, and Inverse Gaussian distributions, directly linking the mode to a linear predictor. Maximum likelihood estimation is performed using the censored log-likelihood, with asymptotic inference based on the observed Fisher information matrix. A Monte Carlo simulation study across multiple distributions, sample sizes, and censoring levels confirms consistent parameter recovery. Empirical bias and RMSE decrease as expected, and Wald confidence intervals achieve nominal coverage. Finally, the proposed methodology is illustrated through an application to real-world reliability data. All methodology is implemented in the open-source R package ModalCens.