BENG449 Problem 6 3

BENG449 Problem 6 3 - X T X b = b X T X-1 X T y-I b = X T X-1 X T y This last result is the familiar formula for the OLS estimate of a linear

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BENG449 – Problem Set 6, Question 3 Alex Lemon March 11, 2008 The Gauss Formula for iterative nonlinear OLS parameter estimates is: b k = b k + ( X T k X k ) - 1 X T k ( y - η k ) Consider the case of a linear model, such that η = Xβ. In terms of the parameter estimates and the context of the iterative algorithm, η k = X k b k . Applying this assumption to the Gauss Formula at k = 0 yields b k = b k + ( X T k X k ) - 1 X T k ( y - η k ) b 1 = b 0 + ( X T 0 X 0 ) - 1 X T 0 ( y - X 0 b 0 ) = b 0 + ( X T 0 X 0 ) - 1 X T 0 y - ( X T 0 X 0 ) - 1 (
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Unformatted text preview: X T X ) b = b + ( X T X )-1 X T y-I · b = ( X T X )-1 X T y This last result is the familiar formula for the OLS estimate of a linear model. Thus, independent of the initial guess b , the Gauss formula converges to the OLS solution after one step for a linear model. 1...
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This note was uploaded on 07/19/2008 for the course BENG 449 taught by Professor Richardcarson during the Spring '08 term at Yale.

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