بر روی نرمال بودن ضریب برآوردگرهای رگرسیون هسته حالت در مدل طراحی تصادفی غیر پارامتری

In the nonparametric regression model with random design, where the regression function m is given by , estimation of the location θ (mode) of a unique maximum of m by the location of a maximum of the Nadaraya–Watson kernel estimator m̂ for the curve m is considered. Within this setting, we obtain consistency and asymptotic normality results for under mild local smoothness assumptions on m and the design density g of X. The estimation of the size of the maximum is also considered as well as the estimation of a unique zero of the regression function. As a by-product, we obtain an asymptotic normality result for the Nadaraya–Watson estimator itself which improves on previous results.