[MASA01] [Matematisk statistik] [Matematikcentrum] [Lunds universitet]

MASA01B: Basic course part B (inference theory)

Current information (last updated: 21 January 2016):

    New date for resit exam (please see below)
    January exam with the sketch of solutions

Institution/Avdelning: Matematikcentrum, Matematisk Statistik


Lectures: Tuesday, Wednesday 1315-1500
Exercises: Friday 1015-1200
Room:
Various!

Textbook:
Michael J. Evans, Jeffrey S. Rosenthal. Probability and Statistics: The Science of Uncertainty, 2nd edition

Course plan (Sections 5, 6, 8, 9,10 in the book):

Lectures
Subject
1 Introduction, statistics as functions of sample and of distribution functions, Riesz theorem
2 Properties of estimators (incl. asymptotic), method of moments (6.3.1, 8.1 first page, 6.4.1)
3 Method of moments (cont.), Maximum likelihood methods (6.4.1, 6.2)
4 Least Squares, Estimators of standard distributions (and of distributions) (10.3.1, 6.2)
5 Confidence intervals, general methods for confidende intervals, reference variables (6.3.2)
6 Confidence intervals (cont.), Hypothesis testing: basics, Test variables method. (5.5.3, 6.3.3)
7 Hypothesis testing: confidence interval method, likelihood ratio test (8.2 except 8.2.4)  Handout
8 Sample distributions (t,χ2), inference for normal distribution (4.6)
9 Inference for normal distribution (two samples, see e.g. this or this or this), normal approximation (4.4.1-4.4.2)
10 Binomial distribution (see this and this), Paired sample (this and this). Poisson distribution (this and this). Read also http://is.gd/uwuxif
11 Non-parametric methods: goodness of fit. (9.1, this, this).  Handout; see also a proof
12 Homogeneity test, test of independence (this, this), Fisher's exact test. (9.1), handout
13 Simple linear regression (10.3-10.3.2)
14 Simple linear regression (cont.), multiple linear regression (10.3.4)

Exercises /  Övningsschema:

For 13 November: 6.2.3, 6.2.11, 6.2.14, 6.2.24, 6.3.13, 6.3.15, 6.3.24, 6.4.2, 6.4.3, 6.4.5

For 27 November: 6.2.26, 6.3.6, 6.3.9, 6.3.11, 6.3.26, 8.2.4, 8.2.5, 8.2.7, 8.2.21, 4.6.4, 4.6.10, 4.6.19

For 15 December: 6.5.4, 6.5.8, 8.2.3, 8.2.5, 9.1.4, 9.1.5. Problems 1 and 2 at the end of this. Do women live more than men? Use paired test with data from here. For these data, test if the data for men are normally distributed; also test if the differences are normally distributed.

For 16 December: 10.3.4 except (g); 10.3.5, 10.3.6 except (h,j), 10.3.20, 10.3.22, 10.3.27.  Also you can estimate a linear regression on a data of your choice where you believe there's a linear relationship (e.g. life expectance and logarithm of GDP, per country).

Labs:

Examination:

Written exam / Skriftliga tenta, Wedenesday 13 January 2016, 1400 - 1900 in Sparta C.

Resit exam / omtenta: Thursday 16 February 2016, 800 - 1300 in MA:09A.

No help materials will be allowed on the exam, except a calculator / inga hjälpmedel tillåts förutom miniräknare och statistiska tabeller vid behöv.

Lecturer for Fall 2015: Stanislav Volkov