Asymptotic normality of the regression mode in the nonparametric random design model for censored data

In the nonparametric regression model, where the regression function m(·,ψ) is given by m(x,ψ)=E(ψ(Y)|X=x)), for a measurable function ψ:R→R, estimation of the location θ (mode) of a unique maximum of m(·,ψ) by the location θ̂n of a maximum of the Nadaraya-Watson kernel estimator m̂ψ,n(·) for the curve m(·,ψ) is considered. Within the setting of the censored data, we obtain the consistency with rate and the asymptotic normality results for θ̂n under mild local smoothness assumptions on the regression m(·,ψ) and the design density of X. Simulation results are performed to illustrate the performance of the procedure.