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Unformatted text preview: Hints for Assignment 2 Ling Chen November 5, 2008 2.9. You may assume that you can interchange integration with differentiation. 3.2. Using the notations Y = ( y 1 ,...,y n ) T , X = 1 ··· 1 x 1 ··· x n , B = ( α,β ) T and E = ( 1 ,..., n ) T , we can write (3.24) as Y = XB + E , and the OLS estimate for B is ˆ B = ( X T X )- 1 X T Y . You can prove (3.27) by following the arguments in Section 2.3.3 and using Definition 2.3 of Wishart distribution. The only thing that might make the multivariate case more complicated is the following: Lemma. Suppose E = ( 1 ,..., n ) T , in which t are i.i.d. N (0 ,V ), W = AE and Z = BE , where A and B are a × n and b × n matrices. Then w i , the i-th row of W , and z j , the j-th row of Z are jointly normal withe mean 0 and Cov( w i ,z j ) = ( AB T ) ij V , where M ij is the ( i,j )-th entry of matrix M . In particular, w i ∼ N (0 , ( AA T ) ii V )....
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This document was uploaded on 11/08/2009.
- Fall '09