This exercise fills in the details of the derivation of the asymptotic distribution of 1 given in Appendix 4 3 a Use Equation (17 19) to derive the expression where vi (Xi X)ui b Use the central limit theorem, the law of large numbers, and Slutsky 's theorem to show that the final term in the equat...

a Using Equation 1719 we have by defining v i X i X u i b The random variables u 1 u n are iid with ...

This exercise fills in the details of the derivation of the asymptotic distribution of 1 given in

Question:

This exercise fills in the details of the derivation of the asymptotic of Î²1 given in Appendix 4.3.
a. Use Equation (17.19) to derive the expression

where vi = (Xi - Î¼X)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)

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

Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...