ON THE BOUNDARY-BEHAVIOR OF NONPARAMETRIC REGRESSION-ESTIMATORS

In this note the nonparametric regression estimators of NADARAYA (1964) and WATSON (1964), PRIESTLEY & CHAO (1972) and GASSER & MULLER (1979) are compared with respect to the boundary behaviour in the case of a fixed design. It is shown that the estimator of Nadaraya & Watson yields estimates with smaller mean squared error at the boundary in finite sample situations compared to the convolution type estimators. By a modification of the kernel function the estimator of Gasser & Muller attains a similar boundary behaviour as the Nadaraya & Watson estimator. The theoretical results are illustrated in a simulation study.