Timing
4 hours weekly (3+1) during Summer Terms.

Lecturer
Herwig Friedl .

Teaching Aims
To provide further results and techniques in the field of mathematical statistics which will be used in other lectures. To improve the student's ability to use this theory in data analysis and statistical modelling. To introduce and learn how to work independently with statistical software packages like R.

Learning Objectives
Students should be able to analyse small studies by their own. They should be also familiar with the concepts of exploratory data analysis and know some basic nonparametrical techniques, find and verify relationships in the data by applying the ideas of statistical modelling.

Contents
(1) Introduction: Computational and Statistical Aspects. (2) Univariate Samples: Nonparametric Estimation, Confidence Intervals and Tests, Density Estimation, Graphical Data Analysis. (3) Comparing two Univariate Samples: Graphical Techniques, Nonparametric Tests. (4) Two-sample Problem: Nonparametric Tests, Smoothing Techniques, Correlation and Independence, Nonparametric Tests, Contingency Tables. (5) k-sample Problem: Oneway and Twoway Classification. Nonparametric Tests for independent and dependent samples. (6) Resampling Techniques: The Boostrap and the Jackknife.

Prerequisites
Probability Theory, Mathematical Statistics, Regression Analysis, Applied Statistics.

Classes

• Monday, 16.00 - 17.30, Seminar Room, Kopernikusgasse 24/III
• Tuesday, 16.00 - 17.30, Seminar Room, Kopernikusgasse 24/III

Homework Assignments

• Homework 1 (due date: March 15th, 2016)
• Homework 2 (due date: April 11th, 2016)
• Homework 3 (due date: May 10th, 2016)
• Homework 4 (due date: May 24th, 2016)
• Homework 5 (due date: May 24th, 2016)

Literature

• Friedl, H. (2005) Computational Statistics. Lecture Notes (in German). Institute of Statistics, 2005.
• Friedl, H. (2005) Computational Statistics. Tables (in German). Institute of Statistics, 2005.
• Davison, A.C., and Hinkley, D.V. (1997) Bootstrap Methods and their Application. Cambridge University Press.
• Venables, W.N., and Ripley, B.D. (2002) Applied Statistics with S (4th Edition). Springer. New York.
• Büning, H., und Trenkler G. (1994) Nichtparametrische Statistische Methoden (2. Auflage). Walter de Gruyter. Berlin.

Software Information
We will use the statistics software 'R'. Here are some helpful links about this statistical package:

• An Introduction to R
• R Reference Manual
• R Installation and Administration
• R Data Import/Export
• R Language Definition

Data

• Aimu, and Data Definition
• Gainesville House Prices, and Data Definition

Additional Lecture Notes

• Remarks on the Minimum Chisquare Method (pdf file),
• Some statements discussed during the R Introduction Session (txt file),
• An Introduction to R with lots of Code (pdf file),
• Some Remarks on MC Simulation and the Bootstrap (pdf file),
• Parametric Bootstrap Tests (air-conditioning example)
• Monte Carlo Tests (overdispersed counts)
• Trimmed Mean Example

Slides used in class

• Slides on Chapter 2 (pdf file)
• Slides on Chapter 3 (pdf file)
• Slides on Chapter 4 (pdf file)
• Slides on the Bootstrap (pdf file)
• Slides on the Monte Carlo Method (pdf file)