Syllabus

I. Course description:

This course provides an introduction to nonparametric statistical methods. We address the problem of estimating unknown 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 finite-dimensional vector of parameters to be estimated, but rather only generic properties such as continuity or differentiability of the functions of interest. Such conditions still allow for smoothing away random sampling noise to obtain a reasonable estimate of the function of interest. We discuss the technical issues associated with nonparametric estimation such as reduced rates of convergence or finding the optimal degree of smoothing. We also touch on resampling methods and
nonparametric test ideas.

After successfully taking this class, you will be able to understand and analyze the advantages and disadvantages of common nonparametric estimation methods, as well as apply them in practice. This course is a good prerequisite for master theses under my guidance.

II. Prerequisities:

Advanced Statistics I & II or equivalent

III. Contents:

  1. Preliminaries
  2. Estimating CDFs and Statistical Functionals
  3. The Bootstrap
  4. Estimating PDFs
  5. Nonparametric Regression
  6. Nonparametric Testing Problems
     

IV. Materials

  • Slides and videos 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: 
    - Chernick, M. R. and R. A. LaBudde (2011). An Introduction to Bootstrap Methods with Applications to R. Wiley.
    - Henderson, D. J., and C. F. Parmeter (2015). Applied Nonparametric Econometrics. Cambridge University Press.
    - Ruppert, D., M. P. Wand and R. J. Carroll (2003). Semiparametric Regression.Cambridge University Press.
    - Wasserman L. (2006). All of Nonparametric Statistics. Springer.

 

VI. Schedule

  • course, 2 hrs. per week; there will be new videos each week, and the original time slot is used for live Q&A (BigBlueButton)
  • pen&paper tutorial: 2 hrs. every second week (videos)
  • non-compulsory computer class: 2 hrs. every second week (videos)
  • see univis for exact times of the live sessions!