ON LOCAL SMOOTHING OF NONPARAMETRIC CURVE ESTIMATORS

We develop new local versions of familiar smoothing methods; such as c ross-validation and smoothed cross-validation, in the contexts of dens ity estimation and regression. These new methods are locally adaptive in the sense that they capture smooth local fluctuations in the curve by using smoothly varying bandwidths that change as the character of t he curve changes. Moreover, the new methods are accurate, easy to appl y, and computationally expedient.