Timing
4 hours weekly (3+1) during Summer Terms.
Lecturer
Herwig Friedl .
Teaching Aims
To introduce into the ideas of nonparametrical statistical inference for
one- and two-sample problems. To discuss some of the classical
nonparametrical tests and compare their power and their efficiency with
those based on normal distributed samples.
Learning Objectives
Students should be familiar with the generel theory in testing hypotheses
and should be able to choose the appropriate procedure to test a special
hypothese. They also should get insight into some modern computer
intensive resampling methods like (parametric and nonparametric)
bootstrapping and jackknifing in order to construct estimates or
confidence intervals for the parameter of interest.
Contents
(1) Theory of Testing Hypotheses: Randomized versus Nonrandomized
Tests; Neyman-Pearson Lemma; Uniformly Most Powerful Tests;
(Asymptotic) Relative Effivciency.
(2) Ordered Samples and Ranks: Ties; Empirical Distribution
Function; Distribution of Ranks and Quantiles.
(3) The One-Sample Problem: Goodness-of-Fit Tests; Tests concerning
Quantiles; Testing Randomness; Confidence Intervalls.
(4) The Two-sample Problem: Independent Samples; Dependent Samples.
Locally Most Powerful Tests.
(6) Resampling Procedures: Introducing the Jackknife and the
Bootstrap; Functional Statistics; Estimating Bias and Variance
by the Jacknife; The Nonparametric Boostrap; Monte-Carlo Method;
MLE and the Parametric Boostrap;
Pre-requisites
Probability Theory, Mathematical Statistics.
Literature