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. Estimation of the distribution of airborne mercury about an incinerator using biomonitoring data. Because of substantial heteroskedasticity, this example requires estimation of the conditional variance function as well as the conditional expectation function. Estimation of gradients from elevation data.