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) and rejects the other A test is called simple , if P 1;P 2 are singletons The worstcase risk of a test is dened as the maximum of the worstcase typeI and typeII errors (T jP 1;P 2) = max sup P 1 2P 1 P 1 f!. N 2ndG U B S Ҍ U A N G X g ʍU A e f ^ A A C e @ A p ` f A I t f Ȃ l g o Q ̎ ȕύX _ @ @ Q T v @ I g A C @ u i K N K v ̐V X ^ @ @ h Ԃ Z k @ ʂ u f v ȂǐV N G X g @ V t B h u C v @ l g o Q ̃f ^ p @ ̑. G = 8 g 2G I Formalizes notion of a symmetric model I Fixed point subspace W G = g T g = 8 g 2G 7/18 Fixed Point Subspace Projection I Statistical model X ˘N(0;) , 2Rp p I Symmetry 2W G I Model Selection Given iid samples X1;; recover n= 1 n i=1 X iX T I HighD regime (n ˝p), n apoor estimate I Gempirical covariance=^ P G (n) I Main contribution statistical.
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