- Date de réalisation : 4 Juillet 2019
- Lieu de réalisation : École Normale Supérieure, Paris.
- Durée du programme : 55 min
- Classification Dewey : Statistique mathématique
- Auteur(s) : Carpentier Alexandra
- producteur : Boyer Claire, Chafaï Djalil, Lehec Joseph
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Carpentier - Introduction to some problems of composite and minimax hypothesis testing
A fundamental question in statistics is: how well can we fulfil a given aim given the data that one possesses? Answering this question sheds light on the possibilities, but also on the fundamental limitations, of statistical methods and algorithms. In this talk, we will consider some examples of this question and its answers in the hypothesis testing setting. We will consider the Gaussian model in (high) dimension p where the data are of the form X = \theta + \sigma \epsilon, where \epsilon is a standard Gaussian vector with identity covariance matrix. An important hypothesis testing question consists in deciding whether \theta belongs to a given subset \Theta_0 of R^p (null hypothesis) or whether the l_2 distance between \theta and the set \Theta_0 is larger than some quantity \rho (alternative hypothesis). We will investigate how difficult, or easy, this testing problem is, namely how large \rho has to be so that the testing problem has a meaningful solution - i.e. that a non-trivial tests exists. We will see through several examples that the answer to this question depends on the shape of \Theta_0 in an interesting way.