Locally Weighted Polynomial Estimation of Spatial Precipitation

We demonstrate the utility of locally weighted polynomial regression, a nonparametric technique for surface estimation discussed in Lall et al. (1995), for the spatial estimation of precipitation surface, with data related to the Chernobyl nuclear power plant accident. The method uses multivariate, locally weighted polynomial regression with temperature or precipitation as the dependent variable and a feature vector (location, elevation and other attributes) of explanatory variables. Localization of the regression is achieved by using k nearest neighbors of the point of estimate and a monotonic distance based weight function. Generalized cross validation is used to pick the order of the polynomial fits, as well as the number of neighbors to use. Pointwise estimates of predictive risk are also obtained.