Local Polynomial Regression and Its Applicationsin

Nonparametric regression estimates a conditional expectation of a response given a predictor variable without requiring parametric assumptions about this conditional expectation. There are many methods of nonparametric regression including kernel estimation, smoothing splines, regression splines, and orthogonal series. Local regression ts parametric models locally by using kernel weights. Local regression is proving to be a particularly simple and eeective method of nonparametric regression. This talk reviews recent work on local polynomial regression including estimation of derivatives, multivariate predictors, and bandwidth selection. Three applications to environmental science are discussed: 1. Estimation of the distribution of airborne mercury about an incinerator using biomonitoring data. 2. Estimation of airborne pollutants from LIDAR (LIght Detection And Ranging) data. Because of substantial heteroskedasticity, this example requires estimation of the conditional variance function as well as the conditional expectation function. 3. Estimation of gradients from elevation data. The estimated gradients are used in a model to predict soil movement during earthquakes. Data from Noshiro, Japan are used. The rst and third examples use two-dimensional spatial data. Though these problems could be analyzed by geostatistics, local polynomial regression has the advantage of modeling the heteroskedasticity in the rst and second examples and being able to estimate gradients in the third.