## Statistical Inference I (7.5 hp) Ph.D. course for students in Statistics, Mathematical Statistics, and related areas - Fall 2023 |

**Components:** 20 Lectures, 5 Tutorials, 10 Homework Assignments

**Organization:** There will be five sessions as listed in the schedule below.

- Krzysztof Podgórski , Department of Statistics, Lund University, e-mail: Krzysztof.Podgorski@stat.lu.se is responsible for the first three sessions and the material associated with them.
- Per Gösta Andersson , Department of Statistics, Stockholm University, e-mail: per.gosta.andersson@stat.su.se is responsible for the remaining two sessions and the material associated with them.
- The first three sessions will be hybrid: in class in Lund and online through Zoom. The lectures of the first three sessions will be recorded and the recording will be made available after the sessions.
- Students outside of Lund are very much welcome to come to Lund to participate. In particular, Session 2, Nov. 16-17 is planned to accomodate both research and social interaction. The cost of travel and accommodation is on your home institution.
- The entirely distant participation is also possible.
- The schedule of the remaining two sessions at Stockholm is approximate and information on their timetable and organization will be given by Per Gösta Andersson.

**Textbook:**

The lecture will be entirely based on the following textbook

- Bickel, Peter J.; Doksum, Kjell A. Mathematical statistics, basic ideas and selected topics. Vol. 1. Second edition. Texts in Statistical Science Series. CRC Press, Boca Raton, FL, 2015.

Session # and location | Date and time | Topic | Supporting material and comments | Assignment |
---|---|---|---|---|

1 Small Seminar Room, EC1-353 and online - Zoom | Friday, November 10, 13:15-15:00 | Introduction -- Data, models, parameters, and statistics, Bayesian set-up. | Sections 1.1, 1.2, and 1.3 of the textbook. Lecture 1 Slides and Lecture 2 Slides | 1.1.1, 1.1.3, 1.1.4, 1.1.6, 1.1.9, 1.2.3, 1.2.6, 1.2.11, 1.2.12, 1.2.14, 1.2.15, Due on the 24th of November |

Friday, November 10, 15:15-17:00 | Sufficiency and exponential Families, Maximum likelihood estimation | Sections 1.5 and 1.6 of the textbook, Sections 2.2-4 of the textbook Lecture 3 Slides and Lecture 4 Slides | 1.5.2, 1.5.3, 1.5.7, 1.5.15, 1.5.16, 1.6.2, 1.6.5, 2.2.10, 2.2.11, 2.2.12, 2.2.14, 2.2.15, 2.2.16a, 2.4.1, 2.4.2, 2.4.4, 2.4.5, Due on 24th of November | |

2 Small Seminar Room, EC1-353 and online - Zoom | Thursday, November 16, 13:15-15:00 | General theory of estimation. | Section 3.4 of the textbook Lecture 5 Slides | 3.4.1, 3.4.5ac, 3.4.10, 3.4.11, 3.4.12, Due on the 15th of December |

Thursday, November 16, 15:15-17:00 | Consistency and efficiency. | Section 5.2.2, | ||

Friday, November 17, 08:15-10:00 | Testing hypothesis and the Neyman-Pearson lemma | Section 4.1-2 of the text Lecture 6 Slides | 4.1.1, 4.1.3, 4.1.4, 4.1.5, 4.1.6, 4.2.2, 4.2.3, 4.2.8, 4.2.9, Due on the 15th of December | |

Friday, November 17, 10:15-12:00 | Uniformly most powerful tests, Confidence regions. | Sections 4.3-5 of the text Lecture 7 Slides and Lecture 8 Slides | 4.3.1, 4.3.2, 4.3.4, 4.3.6, 4.4.1, 4.4.5, 4.4.6, 4.4.10, 4.4.14, 4.5.1, 4.5.2, 4.5.12, Due on the 15th of December | |

Friday, November 17, 12:15-16:00 | Common lunch, round table discussion, conclusions | The assigned problems from Chapter 1 and 2 of the textbook. | The assigned problems from Chapter 1 and 2 of the textbook. | |

3 Small Seminar Room EC1-353 online - Zoom | Friday, November 24, 10:15-12:00 | Frequentist and Bayesian formulations, Prediction intervals | Section 4.7, Section 1.2, Section 1.6.3, Section 4.8 of the text Lecture 9 Slides and Lecture 10 Slides | 4.7.1, 4.7.2, 4.7.3, 4.7.4ab,4.8.1, 4.8.2, 4.8.3 Due on the 15th of December |

Friday, November 24, 13:15-14:00 | Likelihood ratio procedures, Asymptotical Consistency, Discussion | Section 4.9.1-4 Section 5.2.1 Lecture 11 Slides | Some comments and tips | |

4 | TBA | The Delta Method with Applications | TBA | TBA |

TBA | Asymptotic Theory in One Dimension | TBA | TBA | |

TBA | Inference for Gaussian Linear Models | TBA | TBA | |

5 | TBA | Large Sample Tests and Confidence Regions | TBA | TBA |

TBA | Generalized Linear Models | TBA | TBA |

**Homeworks** will serve as a training for the final examination and covering portions of the material as indicated in the above schedule.
They can contribute maximum 40% of the total score for the course.
Each assignment is made of the list of problems. There is also a link to some solutions (not necessary perfect). The homework assignment requires: 1) Grading all provided solution for each problem on the scale from 1 to 10; 2) Choosing three problems from the list that did not receive grade 10 and providing a solution that aims at improving the score. If there are enough problems on the list to improve (graded below 10), then find problems from the text from the same section but that are not on the list and provide solutions to these problems. After the submission of the grading they will be summarized in a table with averaged grades, and your solutions will be graded by your peers and added to the list of grades.

**Final Take-home Exam** will serve as the main assessment of acquired knowledge during the course. The solutions will yield maximum 60% of the total score. After returning the take-home exam there will be scheduled a 15 min conversation with each participant of the course about the solutions to the exam and homework problems. After this the final grade will be assigned. It will be a passing grade if at least 55% of the total score is collected. The final exam will be chosen from the problems on the list and selected individually based on the obtained submission of assignment in a way that will seek an improvement of both the grades and the solutions.

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