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. Nonparametric estimation. Goodness of fit tests

2. Introduction to statistical inference

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

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

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

Offline teaching

This year we don't have to fight with the infrastructure for online teaching. Therefore, all classes will be onsite, à la 2019. I won't be checking attendance.

It is a right of all of you not to attend my lessons (e.g., if you need to work to pay for your studies, or if you just prefer enjoying your youth than listening to a guy talking about stuff), so I will be making any script we use at class available via Github on: https://github.com/fer-cp/usc_inference . Anything else of interest we do during class will either be added here, be an easy follow-up from Prof. Sánchez's notes on the USC online campus, or come directly from the UNED book on statistical inference (Principios de inferencia estadística, by Ricardo Vélez and Alfonso García; paperback copies available at the USC library).

Bootleg

As there are already really good course materials provided by my colleagues, I don't see the need for adding much more, but the following couple of items might be of interest.

You may find the following primer on random variables by EPFL of interest: http://smat-files.epfl.ch/courses/stat/Probability_Overview.pdf .

This is a great course on statistical inference written by UC3M professor Eduardo García-Portugués, which covers the exact same topics we're studying: https://bookdown.org/egarpor/inference/ .

If you are feeling really adventurous, learn how to create an Rmarkdown report for your R code endeavours: https://r4ds.had.co.nz/r-markdown.html . This is a skill that will make your life much easier when organising code and results, and that is very much appreciated in the job market.

Below you have a detailed document explaining how to compute the sampling distribution of the range of a uniform variable that was asked for a few years ago. 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! That said, I tend to write the material that directly targets students in Galician, since someone has to use our language in higher education (the USC is the only university in the world where one can study a BSc in mathematics in Galician!). Derivatives of older work by myself can also be in Spanish, given that I did not hold so strong linguistic viewpoints in the past.

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 ( 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 2023 or 2026.

4. Do you know what you're doing at your classes? Erm, well, the exercises we're doing are by Profs. Rodríguez ( alberto.rodriguez.casal@usc.es ) and Sánchez ( cesar.sanchez@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 they 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 to the exercises or on what I say in class, you'll receive 0x$1... No, not really (I can't afford it) — you'll receive an infinitesimal reward on your grades. :3