Nonparametric Curve Estimation. Lecture 4-5

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 4-5.
Nonparametric tests. Nonparametric tests based on L_2 and sup-norms; asymptotic theory; asymptotic power; bootstrap tests; wild bootstrap.
Well-posed inverse problems. Additive models; empirical integral equation; plug-in estimators of integral equations; backfitting and smooth backfitting estimators; asymptotic theory.