## Messages

The exercise hours in week 34 and 35 will be used for lecturing. These lectures will be on Thursdays from 9:15-10 in H1.

21.08: Chapter 1. Probability and distributions.

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

24.08: Expectation and momentgenerating function.

28.08: Momentgenerating function and Differentiation under an Integral sign. Chapter 2.4.

29.08:Chapter 2.4 Differentiations and sums. Sums and integral. Chapter 3: Commmon families of distributions

31.08: Chapter 3: 3.1-3.3 Common families of distributions Slides week 35

04.09: Gamma,beta, normal and lognormal distribution. Chapter 3.4 Exponential family of distributions

05.09: Chapter 3.4 Exponential family of distributions. Chapter 3.6 Inequalities

11.09: No lecture. Self study: Chapter 3.5, 4.1 4.2

12.09: No Lecture. Self study: Chapter 3.5, 4.1, 4.2

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

19.09: Chapter 4.4 and 4.5: Hierarchical models, mixture distributions and covariance and correlations

25.09: Chapter 4,6 and 4.7: Multivariate distrubution and Inequalities. Random samples 5.1-2

26.09: Chapter 5.1-5.3. Random samples

02.10: Chapter 5.3: Chisquare, t and F distribution

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

09.10: Chapter 5.5.3 and 5.5.4; Convergence in distribution and the Delta Method

10.10: Chapter 5.5.4 and 6.2.1 The Delta Method and sufficiency. Summary Chapter 5

16.10: Chapter 6.2.1 and 6.2.2 Sufficient and minimal sufficient estimators.

17.10: Chapter 6.2.2 Minimal sufficient and Complete statistics

23.10; Chapter 7.2.1-7.2.3: Maximum likelihood, invariance and Bayes estimator. Repetition week 42

24.10: Chapter 7.2.2 and 7.2.3 Invariance and Bayes estimator Bayes and the normal distribution in details

30.10: Chapter 7.2.3 and 7.3.1 and 7.3.2: Bayes estimator, MSE and Cramer-Rao. Repetition week 43

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

06.11: Chapter 7.3.3 Sufficiency and Unbiasedness. 10.1.1 10.1.2. Efficiencies of MLE. 8.2.1 Likelihood ratio test. Repetition week 44

07.11: Chapter 8.2.2. Methods of finding tests. Chapter 8.3. Methods of Evaluating tests. Chapter 10.3, Theorem 10.3.1

13.11: Chapter 8.3.2 Most powerful tests, Neymann-Pearson. Chapter 9.1. Confidence intervals. Chapter 9.2 Methods of finding confidence intervals Repetition week 45

14.11: Chapter 9.2.1 and 9.2.2. Inverting the LRT and Pivotal quantities

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

21.11: Summary of the curriculum slides from the last lecture

21.12: The exam with suggested solution

## Lectures

Mondays: 12.15 - 14.00 in KJL4, In week 34 in room R90, realfagsbygget

Tuesdays: 11:15-13:00 in room KJL4.

## Exercises

Thursdays 09:15-10:00 in room H1. First time 07.09.

Exercise 1, 07.09: 2.33ac, 2.35, 2.38, 3.28abd, 3.39 lf

Exercise 2. 14.09: 3.20, 3.23, 3.30a, 3,46, 3.47 (Hard, but try to come Close). lf

Exercise 3: 21.09: 4.1, 4.4, 4.10, 4.34, 4.56, 5.11 lf

Exercise 4: 28.09: 4.15, 4.30, 4.31, 4.32, 4.35, 4.36, 4.58 lf

Exercise 5: 04.10: 5.6, 5.17, 5.31, 5.35 lf

Exercise 6: 11.10: 5.36, 5.43a), 5.44, 6.1 lf

Exercise 7: Exercise 7 lf

Exercise 8: Exercise 8 Note of Rue and Skaflestad 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

Robin Andersen. Email: robina [at] stud [dot] ntnu [dot] no

Angela Maiken Johnsen. Email: angelamj [at] stud [dot] ntnu [dot] no

Rasmus Erlemann. Email: rasmus [dot] erlemann [at] ntnu [dot] no

## Final 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 situationsâ€¦" 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 9., 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

#### Meeting time before the exam

Tuesday December 5 : 12-14

Wednesday December 6: 10-12

Friday December 8 : 12-14