# TMA4295 Statistical inference (Fall 2009)

## Messages

- [08/12] Here is a sketch of the solutions to the exam problems.

- [30/11] Here is the list of main topics for the exam.

- [27/11] The list of main topics for the exam will be posted on Monday.

- [18/11] The curriculum and some exam problems with solutions have now been posted.

- [15/10] There will be no lectures during week 44 (27 and 29 Oct.).

- [25/9] Tuesday next week the TA Rupali Akerkar will step in as a replacement for me.

- [9/9] Next week Prof. Ushakov will step in as a replacement for me.

- [26/8] The lectures tomorrow are cancelled.

- [21/8] The lecture room problem was quickly solved. We have been allocated auditorium F3 in the old Physics Building for our Tuesday lectures 12-14.

- [20/8] The Monday lectures are now moved to Tuesday 12:15-14. The room 922 is in S2 (Math dept). The room is rather small, so I am trying to find a better one.

- [18/8] Due to a collision of the Monday lecture hours with Time Series Models, we shall change the time of the Monday lectures. This will be discussed during the lectures on Thursday (20/8). If you plan to follow the lectures but cannot attend this Thursday, please provide me with your open time slots.

- [17/8] The first
**exercise**lecture will be on Tuesday 25/08-2009 in Room K1-105. Time: 14:15-15.

- [10/8] The first
**lecture**will be on Monday 17/08-2009. Auditorium: KJL3 kl. 12:15-14. VEL MØTT!

## Textbook

- George Casella, Roger L. Berger: Statistical Inference, Second Edition, 2002, Duxbury.

## Lecturer

Professor Arvid Naess. Office: 1144, S2. Email: arvidn@math.ntnu.no

## TA

Rupali Akerkar. Office: 1124, S2. Email: akerkar@math.ntnu.no

## Schedule

: Tuesday 12:15 - 14:00, F3**Lectures**: Thursday 8:15 - 10:00, KJL4**Lectures**: Tuesday 14:15 - 15, K1-105**Exercises**: Monday, December 7, 2009**Exam**

## Curriculum

## Exam Problems

## Lectures

Date | Topic | Textbook | Exercises |
---|---|---|---|

17.08.09 | Probability theory. | Chapter 1: 1.1, 1.2, 1.3 | 1.1, 1.2, 1.4, 1.9, 1.11, 1.13 |

20.08.09 | Probability theory. Expectations and moments. | Chapter 1: 1.4, 1.5, 1.6. Chapter 2: 2.2, 2.3. | 1.33, 1.38, 1.39 |

25.08.09 | Moment generating function. Distribution of transformed RVs. | Chapter 2: 2.1, 2.3, 2.4 | 1.49, 1.52, 2.12 |

01.09.09 | (Families of distributions.) Multiple random variables | Chapter 3: 3.1, 3.2, 3.3, 3.5; Chapter 4: 4.1, 4.2, 4.3, 4.4, 4.6 | 2.1, 2.17, 2.18, 2.19, 2.20, 2.25, 2.31 |

03.09.09 | Conditional distributions, conditional expectation, covariance and correlation, inequalities | Chapter 3: 3.6; Chapter 4: 4.2, 4.4, 4.5, 4.7; Chapter 4: 4.1, 4.2, 4.3, 4.4, 4.6 | 2.15, 3.21, 3.23, 3.25, 4.1,4.2, 4.6, 4.13 |

08.09.09 | Basic concepts of statistics. Sums. Convergence | Chapter 5: 5.1, 5.2, 5.5 | 4.41, 4.42, 4.43, 4.58, 4.63 |

10.09.09 | Convergence. | Chapter 5: 5.5 | 5.5, 5.15, 5.21, |

15.09.09 | Point estimation. MME and MLE. Evaluation of estimators. | Chapter 7: 7.1, 7.2.1, 7.2.2, 7.3; Chapter 10: 10.1.1 | 7.1, 7.2a, 7.6bc, 7.7, 7.8, 7.11 (in (a) only find the MLE) |

17.09.09 | UMVUE | Chapter 7: 7.3.2 | 7.40, 7.41, 10.1 |

22.09.09 | Cramer-Rao. Efficiency | Chapter 7: 7.3.2 | 7.40, 7.41, 10.1 |

24.09.09 | Sufficient statistic | Chapter 6: 6.1, 6.2 | 6.1, 6.3, 6.6 |

29.09.09 | Minimal sufficient statistic. Complete statistic | Chapter 6: 6.2.2, 6.2.4 | 6.19, 6.20, 7.38 |

01.10.09 | Complete statistic. Exponential families. | Chapter 3: 3.4; Chapter 6: 6.2.1, 6.2.4 | 7.37, 10.9b |

06.10.09 | Exponential families. Hypothesis testing. | Chapter 6: 6.2.4; Chapter 8: 8.1, 8.2, 8.3 | 6.21, 6.22 |

08.10.09 | Hypothesis testing. | Chapter 8: 8.1, 8.2, 8.3 | 7.47, 8.1 |

13.10.09 | Hypothesis testing. | Chapter 8: 8.1, 8.2, 8.3 | 8.13, 8.14 |

15.10.09 | Hypothesis testing. | Chapter 8: 8.1, 8.2, 8.3 | 8.16, 8.18 |

20.10.09 | Hypothesis testing. | Chapter 8: 8.1, 8.2, 8.3 | 8.15, 8.27 |

22.10.09 | Hypothesis testing. | Chapter 8: 8.1, 8.2, 8.3 | 8.17, 8.19 |

03.11.09 | Interval estimation. | Chapter 9: 9.1, 9.2 | 8.19 (numerical solutions) |

05.11.09 | Interval estimation. | Chapter 9: 9.3 | 8.23, 8.45 |

10.11.09 | Asymptotic evaluations. | Chapter 10: 10.1, 10.3, 10.4 | 9.1, 9.2 |

12.11.09 | Asymptotics. | Chapter 10: 10.1, 10.3, 10.4 | 9.8, 9.13 |

17.11.09 | Linear regression. | Chapter 11: 11.1, 11.3 | 10.2, 10.3 |