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Adaptive estimation of functionals under sparsity

Presented by: 
Alexandre Tsybakov CREST: Centre de Recherche en Économie et Statistique, Université Pierre & Marie Curie-Paris VI
Thursday 18th January 2018 - 09:45 to 10:30
INI Seminar Room 1
Adaptive estimation of functionals in sparse mean model and in sparse regression exhibits some interesting effects. This talk focuses on estimation of the L_2-norm of the target vector and of the variance of the noise. In the first problem, the ignorance of the noise level causes changes in the rates. Moreover, the form of the noise distribution also infuences the optimal rate. For example, the rates of estimating the variance differ depending on whether the noise is Gaussian or sub-Gaussian without a precise knowledge of the distribution. Finally, for the sparse mean model, the sub-Gaussian rate cannot be attained adaptively to the noise level on classes of noise distributions with polynomial tails, independently on how fast is the polynomial decay. Joint work with O.Collier and L.Comminges.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons