Symmetrized kernel estimators of the regression slope

Symmetrized kernel estimators of the regression function developed by Yang (1981) and Stute (1984) possess attractive properties, including consistency and asymptotic normality. We propose and develop a class of kernel estimators of the regression slope, which extend symmetrized kernel estimation technology from estimation of the regression function to estimation of the regression slope. We show that in the non-stochastic design case these estimators are consistent and asymptotically normal.