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(center dot,psi) is given by m(x,psi)=E(psi(Y)vertical bar X=x)), for a measurable function psi:R -> R, estimation of the location theta (mode) of a unique maximum of m(center dot,psi) by the location (theta) over cap (n) of a maximum of the Nadaraya-Watson kernel estimator (m) over cap (psi,n)(center dot) for the curve m(center dot,psi) is considered. Within the setting of the censored data, we obtain the consistency with rate and the asymptotic normality results for (theta) over cap (n) under mild local smoothness assumptions on the regression m(center dot,psi) and the design density of X. Simulation results are performed to illustrate the performance of the procedure.