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SUR11-30-10

# SUR11-30-10 - Seemingly Unrelated Regression Notes Charles...

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Seemingly Unrelated Regression Notes Charles B. Moss December 1, 2010 I thought it may be a good idea to work through the mechanics of the matrix operations in Seemingly Unrelated Regression with respect to the Kronecker products. As a starting point, consider a simple regression model 1 x 11 x 12 0 0 0 1 x 21 x 22 0 0 0 1 x 31 x 32 0 0 0 0 0 0 1 x 11 x 12 0 0 0 1 x 21 x 22 0 0 0 1 x 31 x 32 β 01 β 11 β 21 β 02 β 21 β 22 = y 11 y 21 y 31 y 12 y 22 y 32 . (1) The errors from this regression model can be used to form a residual matrix = y 11 β 01 β 11 x 11 β 21 x 12 y 21 β 02 β 12 x 11 β 22 x 12 y 21 β 01 β 11 x 21 β 21 x 22 y 22 β 02 β 12 x 21 β 22 x 22 y 31 β 01 β 11 x 31 β 21 x 32 y 32 β 02 β 12 x 31 β 22 x 32 . (2) Based on these residuals we can define the estimated inverse of the variance matrix used for the Generalized Least Squares form of the weighting matrix ˆ V 1 = / 3 = ˜ V 11 ˜ V 12

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SUR11-30-10 - Seemingly Unrelated Regression Notes Charles...

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