Warsaw University
March - June 2021

Statistics: Course Information

Course LanguagePolish
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’, or indeed any of the other courses offered by the Mathematical Statistics group at Masters level.

Language I shall prepare the lectures in both English and Polish and put both versions up on the course web page. For on-line lectures, I'll prepare slides, which will be in Polish. For tutorials and computer labs, I‘ll run my groups in English; the other groups will be run in Polish. Class Schedule This year, there are 14 lectures (28 hours) and 14 tutorials (28 hours). There are also 6 computer laboratories (12 hours). The classes take place:
March 2nd, 9th, 16th, 23rd, 30th
April 13th, 20th, 27th
May4th, 11th, 18th, 25th
June1st, 8th
The lectures are 8.30 - 10.00.
My tutorial group is 10.15-11.45.
My lab group takes place bi-weekly, 12.00 - 13.30 on Tuesdays: 9th, 23rd March; 20th April; 4th, 18th May; 1st June.

Zoom Co-ordinates The classes will be held on Zoom. I've booked the Zoom slot Tuesdays 08.30 - 14.00 (to include Lectures, Tutorials and Labs for my group). Join Zoom Meeting
Click here to join the meeting
Meeting ID: 743 0100 1601
Passcode: qpUJR2


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.

Grading Policy

  • 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

The lecture, tutorial and lab notes will appear here. The tutorial exercises and lab exercises are for my group (the Tuesday group). We operate according to the standard Warsaw tradition, whereby the individual tutors are responsible for the content and grading policy for their own tutorial and lab groups. (They may use the exercises below, or they may choose to use different exercises). Click here for the data directory.

Past Exam Papers

Here are two past exam papers from the academic year 2018-2019

Examination: June 2021

The final exam can be found in the links below. Please upload your solutions on the MOODLE page. The deadline is: Monday 28th June 2021, 13.00.

Examination: September 2021

The final exam (September session) can be found in the links below. Please upload your solutions on the MOODLE page. The deadline is: Saturday 11th September 2021, 17.00.

(Last updated: 12th June 2021)