## Messages

The exercise hours in week 34 and 35 will be used for lecturing. These lectures will be on Wednesday from 8:15-9.00 in B3.

20.08: Chapter 1. Probability and distributions.

21.08: Chapter 1 and 2: Distributions, combinatorics, transformations and expectation. Slides week 34

22.08: Momentgenerating function.

27.08: Momentgenerating function, differentiation under an Integral sign. Chapter 2.4. Chapter 3.1-3.2. Commmon families of distributions

28.08: Chapter 3.2-3. Negative binomial, gamma, exponential and Chi-square distributions.

29.08: Beta distribution and Chapter 3.4 Exponential family of distributions. Slides week 35

03.09: Inga førelesing

04.09: Inga førelesing. Om nokon har lyst til å bli med i eit forskningsprosjekt så følgjer det ein kinobillett på kjøpet. Informasjon om forskningsprosjekt.

10.09: Chapter 3.4 Exponential family of distributions. Chapter 3.5. Location and scale families.

11.09: Chapter 3.6 Inequalities. Chapter 4.2 and 4.3 Bivariate distributions Slides week 37

17.09: Chapter 4.3 and 4.4: Bivariate transformations, hierarchical models and mixture distributions.

18.09: Chapter 4.4-4.7: Hierarchical models, mixture distributions and covariance and correlations, inequalities. Slides week 38

24.09: Chapter 4.7: Inequalities. Random samples 5.1-2

25.09: Chapter 5.3: Nomally Distributed random sample, Chisquare distribution and t-distribution Slides week 39

01.10: Chapter 5.3 and 5.5 F-distribution and convergence in probability and distribution

02.10: Chapter 5.5.3 and 5.5.4; Convergence in distribution and the Delta Method Slides week 40

08.10: Chapter 5.5.4 and 6.2.1 The Delta Method and sufficiency.

09.10: Chapter 6.2.1 and 6.2.2 Sufficient and minimal sufficient estimators. Slides week 41

15.10: Chapter 6.2.2 Minimal sufficient and Complete statistics

16.10: Chapter 6.2.2, 7.2.1-7.2.3: Complete statistics and Maximum likelihood. Slides week 42

22.10: Chapter 7.2.1-7.2.3: Maximum likelihood, invariance and Bayes estimator.

23.10: Chapter 7.2.2 and 7.2.3 Bayes estimator, MSE Slides week 43

29.10: Chapter 7.3.2 Cramer-Rao Inequality and Equality. Cramer-Rao in the multiparameter case

30.10: Chapter 7.3.3 Sufficiency and Unbiasedness. Slides week 44

05.11: Chapter 8.2.1 Likelihood ratio test.Chapter 8.3. Methods of Evaluating tests.

06.11: Chapter 8.3.2 Most powerful tests, Neymann-Pearson. Chapter 9.1. Confidence intervals.Slides week 45

12.11: Chapter 9.2.1 and 9.2.2: Methods of finding confidence intervals. Inverting the LRT and Pivotal quantities

13.11: Chapter 9.2.3 and 9.2.4: Pivoting the cdf and Bayesian Interval

19.11: Chapter 9.2.4: Bayesian Intervals. Chapter 10.1.1-10.1.2. Point estimation and efficiency. Confidence interval in the Poisson distribution

20.11: Chapter 10.3.1: Asymptotic distribution of the LRT. Repetition

## Lectures

Mondays: 12.15 - 14.00 in room R4.

Tuesdays: 08:15-10:00 in room B3.

## Meeting hour

Fridays: 14-15

## Exercises

Wednesdays 08:15-09:00 in room B3. First time 05.09. Note that the exercises are not compulsory in the sense

that they will be collected and approved, but they are extemely important for the exam.

Exercise 1, 05.09: 2.33ac, 2.35, 2.38, 3.28abd, 3.39. lf

Exercise 2, 12.09: Exercise 2 lf

Exercise 3, 19.09: 3,46, 3.47 (hard), 4.1, 4.4, 4.10, 4.34. lf

Exercise 4: 26.09: 4.15, 4.30, 4.31, 4.32, 4.35, 4.36, 4.58 lf

Exercise 5: 03.10: 5.6, 5.17, 5.31, 5.35 lf

Exercise 6: 10.10: 5.36, 5.43a), 5.44, 6.1. lf

Exercise 7: Exercise 7
lf

Exercise 8: Exercise 8 Note of Rue and Skaflestad
Bayes and the normal distribution in details
lf

Exercise 9: Exercise 9. lf

Exercise 10: Exercise 10.
lf

Exercise 11: Exercise 11.
lf

Exercise 12: Exercise 12 lf

## Teacher

John Tyssedal, room 1132, SII. Email: John [dot] tyssedal [at] ntnu [dot] no

## Teaching assistant

Jacopo Paglia, room 1001, SII. Email: jacopo [dot] paglia [at] ntnu [dot] no

## Reference group

## Curriculum

The curriculum is defined to be all that is covered in lectures and exercises, as described on the course homepage under "Lecture plan and progress" and "Exercises".

The following list gives references to the planned topics covered from the course book: **Statistical Inference by George Casella and Roger Berger** (Second Edition)

*Chapter 1: Probability theory.* Assumed known

*Chapter 2: Transformations and expectations.* 2.1 (assumed known); 2.2-2.4

*Chapter 3: Common families of distributions.* 3.1-3.3 (assumed known); 3.4, 3.5, 3.6.1

*Chapter 4: Multiple random variables.* 4.1-4.6 (4.5 only partly); 4.7 (only Cauchy-Schwarz and Jensen's inequality)

*Chapter 5: Properties of a random sample.* 5.1-5.3 (not all in detail),5.5.1, 5.5.3, 5.5.4.

*Chapter 6: Principles of data reduction.* 6.1, 6.2.1, 6.2.2, Def. 6.2.21, Examples 6.22.22-23, Theorem 6.2.25

*Chapter 7: Point estimation.* 7.1, 7.2.1, 7.2.2, 7.2.3, 7.3.1 (except from "In certain situations…" on p. 333), 7.3.2, 7.3.3 (from beginning to Example 7.3.18, then from top of page 347 and rest of section 7.3.3; Theorem 7.5.1.

*Chapter 8: Hypothesis testing.* 8.1, 8.2.1, 8.3.1 (except page 387), 8.3.2 until Def. 8.3.16 (only part a in Theorem 8.3.12).

*Chapter 9: Interval estimation.* 9.1, 9.2

*Chapter 10: Asymptotic evaluations.* 10.1.1, 10.1.2, 10.1.3, 10.3.1 to theorem 10.3.3, Score statistic on page 494.

## Exam

The exam will be on December 5., 9.00-13.00. It will be a written exam.
You are allowed to bring with you:

Tabeller og formler i statistikk

NTNU certified calculator

Personal, handwritten, stamped yellow sheet, A5-format. You get the sheet in the Department office, 7. floor

The exam text will contain a collections of results from the text-book as given here

Earlier exams with solutions can be found here:earlier exams

The exam 2017 with suggested solution

The exam 2018 with suggested solution

The curriculum should make you able to solve the problems in most of the earlier exams, but you will meet questions about ARE or Square Loss function in a Bayesian setting in some of them. That is not covered by our curriculum, and you will not meet such questions on the exam.

Meeting hours before the exam in my offfice

Friday 30. November 14-16

Monday 3. December 13-15

Tuesday 4. December 13-15