Question

Suppose you are trying to estimate $Y=\beta_0+\beta_1 X+U$ where you know that the error term is heteroskedastic, so that $E[U|X]\neq \sigma ^2 I$ . Suppose,however, you know from external sources of information (perhaps from administrative procedure in drawing random sample) that the true variance-covariance of the error term is $E[U|X]=\sigma_i^2 I$ and you know the value of $\sigma_i \forall i$ . Suggest a data transformation (changing X and Y) so that you can obtain a bestlinear unbiased estimator of .

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Answer 1

DATE ssion equation whese variance covariance oF emoY E ou divide above equation by Nat 6 6767 This is transfoi med egression equaion where variance covariance afu is 2. twhich is consta.nt.