Nonparametric Curve Estimation. Lecture 1

This course introduces into the basic techniques of nonparametric smoothing. In particular, we discussed kernel smoothing, sieve estimators and smoothing splines. The course discusses applications of the methods in semi parametric models and inverse problems that e.g. arise in nonparametric models with instrumental variables. A further topic is structured nonparametric models where several nonparametric functions enter into a model specification. The aim of the course is an understanding of the theoretical mathematical background of these models and statistical approaches.
Lecture 1. Nonparametric kernel density estimation. Motivation of kernel density estimators; asymptotic theory: limit distributions and rates of convergence; smoothing parameter selection; multivariate density estimation.