Local Polynomial Regression: A Nonparametric Regression Approach

Abstract

In local polynomial regression, the regression coefficient is allowed to change with the value of the explanatory variable, and it is estimated from data that lie within a certain window around x. Only observations within the smoothing window are used to estimate the coefficients of the polynomial. This chapter talks about model selection and application of density estimation and the smoothing of histograms in detail. Local polynomial regression can be used to estimate the density of a distribution. The local polynomial regression can be used when there are two or more explanatory variables in the model. For illustration two examples are used: the eruption and waiting times to the next eruption of 272 eruptions of the Old Faithful geyser in the Yellowstone National Park, and the NOx exhaust emissions when using pure ethanol as the spark-ignition fuel in a single-cylinder engine.