🤖 AI Summary
This study addresses the lack of a unified and interpretable modal regression framework for right-censored positive responses by proposing a parametric modal regression approach applicable to continuous positive distributions—namely Gamma, Beta, Weibull, Lognormal, and Inverse Gaussian. By analytically reparameterizing the density parameters as explicit functions of the conditional mode and integrating the censored log-likelihood for maximum likelihood estimation, the method establishes, for the first time, a closed-form mapping between the mode and a linear predictor under these distributions. The framework enables direct modeling of the conditional mode and facilitates asymptotic inference via the Fisher information matrix. Simulations confirm consistent parameter estimation, with bias and RMSE decreasing as sample size increases, and Wald confidence intervals achieving nominal coverage. The approach is successfully applied to real-world reliability data, and an accompanying R package, ModalCens, is made publicly available.
📝 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.