Nonparametric Regression: Kernel-Based Estimation

This lecture introduces nonparametric regression, where the traditional linear relation between covariates and response variable is replaced by a general function. The approach is nonparametric, requiring an infinite number of parameters to describe the regression function. The lecture covers kernel smoothing techniques, local intercept regression, and local polynomial regression. Different kernel functions and bandwidth selection are discussed to ensure a smooth and accurate estimation of the regression function. The choice of polynomial degree in local polynomial regression is also explored, highlighting the trade-off between model complexity and overfitting. Practical examples and optimization problems are presented to illustrate the concepts.