Multivariate Advanced Statistics (3 ECTS)

Relatore:  Tyll Krüger - Wroclaw University of Technology
  mercoledì 17 ottobre 2018 alle ore 12.30
Multivariate Advanced Statistics [ 3 ECTS ]

Syllabus of the mini course [ tentative ]

1) Intro: Recall basic definitions probability theory and overview about basic problems in
multivariate statistics (classical and modern). Course overview
2) Multivariate law of large numbers, ergodic theorem, discrepancy, Vapnik–Chervonenkis
inequality, VC dimension and all that.
3) Important multivariate distributions and their basic properties (Dirichlet, Normal distribution,
exponential family,…)
4) The multivariate central limit theorem and multivariate Berry Esseen theorem .
5) parametric inference 1: ML estimators for exponential families, asymptotic optimality, Fisher
information, sufficient statistics, Kullback–Leibler divergence
6) The search for best UMV estimators : Cramer - Rao bound , Steins paradox and James - Stein
estimator
7) confidence regions - asymptotic and non asymptotic theory - concentration inequalities 1
8) the concentration of measure phenomenon and it’s use in statistics (Talagrands inequality,
Johnson–Lindenstrauss lemma and other concentration inequalities)
9) Basic Hypothesis testing 1 (normal distribution, exponential family) - special tests related to
normal distribution (Hotelling's T-squared distribution, Wishart distribution)
10) Hypothesis testings 2 (tests for extrema and related concentration inequalities)
11) PCA
12) Linear and probabilistic regression
13) statistical learning theory 1
14) statistical and machine learning 2
15) Neural networks

The provisional timetable is the following:

wednesday 12.30 - 15.30 - friday 15.30 -17.30

Referente
Luca Di Persio

Data pubblicazione
26 settembre 2018

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