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Currently displaying 1 – 2 of 2

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Minimax nonparametric hypothesis testing for ellipsoids and Besov bodies

Yuri I. Ingster; Irina A. Suslina — 2000

ESAIM: Probability and Statistics

Minimax nonparametric hypothesis testing for ellipsoids and Besov bodies

Yuri I. Ingster; Irina A. Suslina — 2010

ESAIM: Probability and Statistics

We observe an infinitely dimensional Gaussian random vector where is a sequence of standard Gaussian variables and is an unknown mean. We consider the hypothesis testing problem alternatives $H_{ε, τ} : v \in V_{ε}$ for the sets $V_{ε} = V_{ε} (τ, ρ_{ε}) \subset l_{2}$ . The sets are -ellipsoids of semi-axes with -ellipsoid of semi-axes removed or similar Besov bodies with Besov bodies removed. Here $τ = (κ, R)$ or $τ = (κ, h, t, R); κ = (p, q, r, s)$ are the parameters which define the sets for given radii , 0 < ; is the asymptotical parameter. We...

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