Welcome to any students and curious people that have somehow decided to drop by! For some of the people taking this course, this will be the most difficult and last statistics lessons you will ever take, so my colleagues and I will try to make the experience as painless, pleasant and formative as possible.

Syllabus

1. Introduction to statistical inference

2. Parametric estimation. Method of moments and maximum likelihood. Fréchet–Cramér–Rao bound. Efficiency

3. Parametric confidence regions. Pivotal, Neyman and asymptotic construction of intervals

4. Parametric hypothesis testing. Optimality in hypothesis testing. Neyman–Pearson lemma. Likelihood ratio test

5. Nonparametric estimation. Goodness of fit tests

Course materials

The USC online campus for the course contains Prof. González-Manteiga's detailed notes for the theoretical classes, as well as several sets of exercises for the problem sessions. My classes will be devoted to refreshing the former and to developing the latter. I might add some materials on this site in the future if I deem it necessary, but in any case the main communication channel will be the USC online campus, so there's no need to check this site for updates.

Video channel

I will be recording all my classes, at least while we maintain the remote learning scenario. From that point on, I'll try to keep doing it, but I can't ensure yet that I'll have the necessary technical resources available at the Faculty of Mathematics, due to high demand.

Bootleg

As there are already really good course materials, I don't see the need for creating much more... However, I'm aware that part of my first classes couldn't be followed very clearly, neither live nor in the recording, due to tech issues. So I've produced a detailed document explaining how to compute the sampling distribution of the range of a uniform variable. The part about the asymptotics is just an addendum, in case anyone wants to learn more than what is required for the exam (for the exam, getting to the beta distribution is more than enough). Once you understand the first 1.75 pages of the document, all the exercises of chapter 1 should be easy for you.

FAQs

1. Why is this site in English? My website is all in English because it's aimed at a general audience; including international colleagues and friends, and exchange students. Plus, you really need to understand mathematics texts in English, if you want to to learn independently in today's world. So don't complain so much!

2. I have doubts related to statistics and/or the course. Can I ask them to you? Although I'm not being paid for these classes and they take time away from my actual and poorly-paid job, I'll be happy to help you learn about any topic that is (in)directly related to my classes. That said, I have no knowledge of how the exams will be nor about the assessment criteria or what happens in the lessons I don't teach. For any purpose related to studying for the course per se, please contact the most appropriate of your real professors ( rosa.crujeiras@usc.es , wenceslao.gonzalez@usc.es , mercedes.amboage@usc.es , alberto.rodriguez.casal@usc.es , cesar.sanchez@usc.es ), depending on who taught what you want to ask about.

3. Can I contact you regarding other issues? Can I contact you once the course is over? Yes and yes. I've received valuable help from university staff in the past, with various personal and academic problems. If you don't know whom else to ask or if you feel that you trust me for whatever reason, please don't hesitate to contact me, regardless of whether we're in 2021 or 2023.

4. Do you know what you're doing at your classes? Erm, well, the exercises we're doing are by Prof. Rodríguez-Casal ( alberto.rodriguez.casal@usc.es ) and I'm just trying to solve them making as few mistakes as possible. For any enquiries regarding the exercises, keep in mind that he can provide you with a better perspective on the exercises, whereas I can only offer a nice attitude and good wishes. If you find any errata on my solutions of the exercises or on what I say in class, you'll receive 0x$1... No, just kidding (I can't afford it) — you'll receive a slight grading reward.