Local Polynomial Regression and Its Applications in Environmental Statistics
David Ruppert · 1996
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 fits parametric models locally by using kernel weights. Local regression is proving to be a particularly simple and effective 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 func...