A New Nonparametic Estimation Method: Local and Nonlinear

In the paper we consider a new class (called NoLoess) of nonparametric estimators of regression function r(x) = E(Y jX = x): The new estimators link nonparametric and parametric methods. NoLoess extends the class of Macauley, Cleveland, and Stone estimators and replaces their locally linear models (Loess) given by (1.3) with a general locally parametric nonlinear model g(x;). The parameter is estimated locally by tting g(x;) to a sub-sample (X i1 ; Y i1); : : : ; (X ik(x) ; Y ik(x)) with X i1 ; : : : ; X ik(x) being close to x. The resulting nonparametric estimator of r(x) is of the form g(x; ^)(x). Under proper regularity assumptions it is strongly consistent. An interactive software package FS 2.0 running under MS DOS on IBM PC and compata-bile, and implementing a variety of nonparametric Loess-and NoLoess-type estimators has been developped.