Warsaw University
March - June 2022

### Statistics: Course Information

Course Type Obligatory Courses

Warning For students who want to study statistics at Masters level, it is important to take the course ‘Statistics’. The course ‘Statistical Data Analysis’ does not give sufficient background in statistical theory for courses such as ‘Multivariate Statistics’ or ‘Time Series’.

## Description

This course gives an introduction to classical statistics. While Bayesian statistics is very important and in many situations a preferable approach, it was decided that the two approaches should be introduced separately, to avoid confusion. (Bayesian statistics is introduced in the Master‘s course Bayesian Statistics given by Wojciech Niemiro. This is an important course and is highly recommended.)

The course covers:
• Statistical Models, non-parametric, semi-parametric, parametric, the empirical distribution, the Kolmogorov-Smirnov test.
• Parameters and Sufficiency: Sufficient statistics, minimal sufficient statistics, complete statistics, factorisation theorem.
• Exponential families and their parametrisations
• Parameter Estimation: Minimum contrast, estimating equation method, maximum likelihood, method of moments, least squares. Kullback Leibler divergence, maximum likelihood as a minimum contrast.
• The information inequality, linear predictors.
• Complete Sufficiency and UMVU (Uniform Minimum Variance Unbiased) estimators.
• Asymptotic results for estimators, consistency, the Delta method.
• Confidence Intervals: Pivot method. Hypothesis Testing: Likelihood Ratio Test, Neyman Pearson lemma, Monotone Likelihood Ratio, Rubin Karlin theorem, p-values, Confidence intervals by inverting a test statistic.
• Gaussian Linear Models
• Asymptotic Likelihood Ratio test, Chi squared tests, Wald statistic, Logistic regression.

• Computer Laboratory This is pass/fail. To pass the course, it is necessary to pass the computer labs.
• Tutorial work will be assessed; the assessment method depends on the tutor. The tutorial grade carries a weight of 30%.
• The final examination carries a weight of 70%.
• The final grade will be based either entirely on the final exam, or 70% final exam / 30% tutorials, which ever gives the higher grade.

## Lecture and Tutorial Notes

Click here for the lecture, tutorial and lab notes.