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Unformatted text preview: X n , i.e., ˆ X n = n-1 X i =1 b i X n-i . Let F be the set all densities f ( x n ) satisfying R ,R 1 ,...,R p . Assume n > p . Find max f ( x n ) min b E ( X n-ˆ X n ) 2 . This identiﬁes the process which is hardest to estimate from the past. 5. Hadamard. Let K be a 2 n × 2 n nonnegative deﬁnite symmetric matrix. Show det( K ) ≤ n Y i =1 det( K (2 i-1 , 2 i )) , where K ( i,j ) denotes the 2 × 2 submatrix ± K ii K ij K ji K jj ¶ . 6. Maximum entropy. (a) What is the parametric form maximum entropy density f ( x ) satisfying the two conditions EX 8 = a EX 16 = b. Don’t solve for the λ ’s. (b) What is the maximum entropy density satisfying the condition E ( X 8 + X 16 ) = a + b ? 2...
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- Spring '05
- Information Theory, Estimation theory, Det, maximum entropy, Kii Kij Kji Kjj