Nonparametric Regression: Local Polynomial Estimation

This lecture introduces nonparametric regression, focusing on local polynomial estimation as a method to estimate regression functions in local terms. The instructor discusses the concept of smoothness in functions and demonstrates the use of kernel smoothing and local linear regression. The lecture also covers the idea of basis function estimation, particularly splines, and explains how penalized least squares can be used to balance fidelity to the data and smoothness in the estimated function. Through examples and mathematical explanations, the instructor illustrates the trade-offs between bias and variance in nonparametric regression methods.