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Unformatted text preview: BENG449 Problem Set 6, Question 6 Alex Lemon March 11, 2008 1 Weighting Terms The model for the generation of observed data is y = ( t ) + If the disturbance terms, i , are homoscedastic, then the ordinary least-squares estimate is the minimum-variance unbiased estimator. On the other hand, this result is not valid if the disturbance terms are heteroscedastic (that is, they have different variances). However, when the variances of the disturbances terms are known to be proportional to some weighting term, w i , then it is trivial to correct for heteroscedastic errors using weighted least squares. In particular, the weighted least squares estimate is obtained by applying ordinary least squares to fit the model y i w i = ( t ) w i + i w i Note that the variance of the modified disturbance terms is constant: Var parenleftbigg i w i parenrightbigg = 1 w i Var ( i ) = c In the present example, the stochastic error terms were generated using a Pois- son process. Recall that the mean and variance of a Poisson process are both given by the distribution parameter, . In particular, the variance of the dis- turbance terms is 2 i = y i Thus, the weighting terms are simply the data values....
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- Spring '08