# I. Course description:

This specialization course provides an introduction to nonparametric statistical methods. We address the problem of estimating unknown \emph{functions} rather than unknown parameters, concretely: cumulative distribution functions, probability density functions, and regression functions. The difference to Advanced Statistics II is that we do not assume a concrete family of distributions characterized by a vector of parameters to be estimated, but rather only generic properties such as continuity or differentiability of the functions of interest that still allow for smoothing sampling noise away to obtain an estimate. We discuss the technical issues associated with nonparametric estimation such as reduced rates of convergence or finding the optimal degree of smoothing. Concerning nonparametric regression, we also discuss semiparametric models combining parametric and nonparametric aspects. After successfully participating, you should be able to understand and analyze the advantages and disadvantages of common nonparametric estimation methods, as well as apply them in practice.

# II. Prerequisities:

Advanced Statistics I & II or equivalent

# III. Outline:

1. Estimating CDFs and Statistical Functionals
1.1  The CDF
1.2  Estimating Statistical Functionals
1.3  Inuence Functions
1.4  Resampling: Jackkniefe & the Bootstrap

2. The Histogram
2.1  Construction
2.2  Properties of the Histogram
2.3  Average Shifted Histogram

3. Estimating PDFs
3.1  Kernel-Based Smoothing

3.2  Statistical Properties
3.3  Selecting the Smoothing Parameter
3.4  Choosing the Kernel
3.5  Confidence Intervals vs. Confidence Bands
3.6  The Multivariate Case

4. Nonparametric Regression
4.1  Univariate Kernel Regression
4.2  Other Smoothers
4.3  Selecting the Smoothing Parameter
4.4  The Multivariate Case
4.5  Some Semiparametrics

5. Nonparametric Testing Problems
5.1  Nonparametric Hypotheses
5.2  Standard Specification Tests
5.3  Conditional Moments Tests

# IV. Materials

• Slides will be made available in due time (OLAT)
• The course follows largely the first part of:

- Härdle, W., A. Werwatz, M. Müller, and S. Sperlich (2004). Nonparametric and Semiparametric Models. Springer.

• Other useful ones:
-  Henderson, D.J., and C.F. Parmeter (2015). Applied Nonparametric Econometrics. Cambridge University Press.

-  Li, Q. and J.S. Racine (2007). Nonparametric Econometrics: Theory and Practice. Princeton University Press.
-  Ruppert, D., M.P. Wand and R.J. Carroll (2003). Semiparametric Regression. Cambridge University Press.
-  Efron, B. and R.J. Tibshirani (1993). An Introduction to the Bootstrap. Chapman & Hall.
-  Wasserman L. (2006). All of Nonparametric Statistics. Springer.

# VI. Schedule

• course, 2 hrs. per week
• tutorial, 2 hrs. every second week
• non-compulsory computer class: every second week (tutored by Anna Titova)
(for this you'll have to choose a slot and will need an account, details in class)
• see univis for exact times and location.