Topics in Statistical Theory

## Yoav Zemel

Part III, Lent 2020.

 example sheet 1 solutions 1 example sheet 2 solutions 2 example sheet 3 solutions 3

February 5: a typo in exercise 5 has been corrected.
February 17: exercise 4 on sheet 2 has been slightly modified, and a typo on exercise 10 has been corrected.
March 18: typos in questions 8 (for the variance of the order statistic), 10e, and 13 have been corrected. Thanks to Joseph Turrini for spotting the first of these!
March 25: typos corrected in solution of sheet 2, question 10a, case (ii) as well as question 13 in sheet 3 (the definition of $\Sigma(F)$ was not correct). Thanks to Zhaomeng Chen for spotting these!

#### Lecture notes

March 25: Three corrections regarding the lectures: 1) In the epsilon / C_\epsilon theorem of Section 2.6, one needs to assume that R(K) is finite. 2) In Section 6.1, the definition of $\Sigma(F)$ should be $E[(X- EX)(X-EX)^t]$. 3) In the proof of Proposition 6.4, it should read $|Ef(X)|-|f(0)|\le E\|X\|\le .... <\infty$. Thanks to Zhaomeng Chen for bringing these to my attention!

Lecture notes (last update: 10.02). Beware that they do not contain everything that I said in class, and sometimes differ from what was written on the blackboard. Note that $D_h$ in the notes is different than the one defined in class! Lecture notes on optimal transport are available separately.

#### Optimal transport lecture notes

Lecture notes written by Louis Christie with some modifications by myself. I am very grateful to Louis for sharing and allowing me to post these on this website. Here is a file containing some measure-theoretical results (Portmanteau and gluing lemma, Prokhorov theorem). The material in this file, including the statements of the results, is not examinable.

#### Non-exmainable material

All course material, including the example sheets, is examinable, with the exception of question 9 in sheet 2, questions 12-13 in sheet 3, regression splines, equivalent kernel (in the context of splines), the comments I made at the beginning of lecture 15 (about the conditional independence in the context of the variance term in the classification problem) and those made at the end of lecture 14 (about the values of $g(K)$ for different functions $K$ in the minimax lower bound example).

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