d 5 points Using the linear combination of independent univariate normals

D 5 points using the linear combination of

This preview shows page 2 - 4 out of 9 pages.

(d) (5 points) Using the linear combination of independent univariate normals result (posted as a hint below homework 1pdf file), find thedistributionof the least squares estimator ofβfound in part (1b) - including the mean and variance.Confirm that your variance expression matches that obtained in part (1c). (e) (5 points) Using 120A/B expectation results in the case of the model above, show thatW=ni=1Yini=1xiis another unbiased estimator ofβ. (f) (5 points) Using 120A/B variance results in the case of the model above, calculate the variance ofWin part (1e), andcompare it to the variance of the ordinary least squares estimator found in part (1b).Hint: If it helps you in this problem, you may assume thatnXj=1x2j(ni=1xi)2n!. 2 2
Image of page 2
Image of page 3
Image of page 4

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture