1. Copyright © 2006 Pearson Addison-Wesley. All rights reserved. Lecture 5: Supplemental

2. Copyright © 2006 Pearson Addison-Wesley. All rights reserved. 5S-2 BLUE Estimators

3. Copyright © 2006 Pearson Addison-Wesley. All rights reserved. 5S-3 To solve this problem for the general case would require linear algebra and multivariable calculus. We can use univariate calculus to solve the case that n = 2. We want to find w 1 and w 2 to minimize   2 (w 1 2 + w 2 2 ) subject to the constraint that w 1 X 1 + w 2 X 2 =1 The constraint implies: BLUE Estimators (cont.)

4. Copyright © 2006 Pearson Addison-Wesley. All rights reserved. 5S-4 BLUE Estimators (cont.)

5. Copyright © 2006 Pearson Addison-Wesley. All rights reserved. 5S-5 BLUE Estimators (cont.)

6. Copyright © 2006 Pearson Addison-Wesley. All rights reserved. 5S-6 BLUE Estimators (cont.)

7. Copyright © 2006 Pearson Addison-Wesley. All rights reserved. 5S-7 BLUE Estimators (cont.)

8. Copyright © 2006 Pearson Addison-Wesley. All rights reserved. 5S-8 BLUE Estimators (cont.)