A Semi-Parametric Mode Regression with Censored Data

In this work we suppose that the random vector (X, Y) satisfies the regression model Y = m(X) + ϵ, where m(·) belongs to some parametric class {mβ(⋅):β∈K\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${m_\beta}(\cdot):\beta \in \mathbb{K}$\end{document}} and the error ϵ is independent of the covariate X. The response Y is subject to random right censoring. Using a nonlinear mode regression, a new estimation procedure for the true unknown parameter vector β0is proposed that extends the classical least squares procedure for nonlinear regression. We also establish asymptotic properties for the proposed estimator under assumptions of the error density. We investigate the performance through a simulation study.