econometrics (Page 309)

# econometrics (Page 309)

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3 This knowledge will help us to draw inferences about the true σ 2 from the estimated σ 2 , as we will show in Chapter 5. (The chi-square distribution and its properties are discussed in Appendix A.) 7.( ˆ β1, ˆ β2) are distributed independently of ˆ σ 2 . The importance of this will be explained in the next chapter. 8. ˆ β1and ˆ β2have minimum variance in the entire class of unbiased estimators, whether linear or not.This result, due to Rao, is very powerful because, unlike the Gauss–Markov theorem, it is not restricted to the class of linear estimators only. 4 Therefore, we can say that the least-squares estimators are best unbiased estimators (BUE);that is, they

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