17.3. This exercise fills in the details of the derivation of the asymptotic distribution of b n

1 given in Appendix 4.3.

a. Use Equation (17.19) to derive the expression

where vi = (Xi - mX)ui.

b. Use the central limit theorem, the law of large numbers, and Slutsky’s theorem to show that the final term in the equation converges in probability to zero.

c. Use the Cauchy–Schwarz inequality and the third least squares assumption in Key Concept 17.1 to prove that var(vi) 6 . Does the term 21n gni = 1 vi>sv satisfy the central limit theorem?

d. Apply the central limit theorem and Slutsky’s theorem to obtain the result in Equation (17.12).

Transcribed Image Text:

n(B - B) = (X-x). (x-x)(x-x)