Treed Kernel Smoothers: Recursive Partitioning of Bandwidths for Local-Linear Regression WILLIAM R. SCHUCANY Southern Methodist University  For nonparametric regression problems with complicated structure a single global smoothing parameter is unsatisfactory.  Specifically, kernel estimators of conditional response means can be improved by adapting to local curvature.  Locally weighted least-squares polynomial fits have been shown to be successful.  However, estimates of variable bandwidths can be a challenging undertaking.  We have previously made some satisfactory progress with piecewise constant bandwidths for local linear fitting and a modified Akaike Information Criterion. Our new proposal extends this approach with a recursive partitioning to simultaneously determine both the interval in the explanatory variable and the bandwidth to be used throughout that interval. The result is a regression tree with separate data-based choices of kernel smoothing parameters applied over adaptively selected regions in the predictor variable.  The new methodology compares well with the variable bandwidth estimators in Fan and Gijbels (1995).