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Unformatted text preview: X n , i.e., 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- X n ) 2 . This identies the process which is hardest to estimate from the past. 5. Hadamard. Let K be a 2 n 2 n nonnegative denite 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. Dont solve for the 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