## Messages

Welcome to the course TMA4295 Statistical Inference. The first lecture will be on Monday, August 21 at 12.15 in room R90.
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