Lecture 6 - Hypothesis Testing only Flashcards
Derive the distributon of n^(1/2)[Beta hat - Beta] with stochastic z’s.
Write the F test statistic (Wald statistic)
Under which circumstances can we make a claim regarding the distribution of the F statistic and to what? Write in detail.
If we don’t assume u_i is iid, what assumptions do we need? List in detail.
Re-write the F statistic given those assumptions.
Make an observation regarding the F statistic and theorems we can use with the given assumptions.
Rewrite the test statistics in terms of what you have derived, and show the denominator derivation in detail.
Derive the distribution of the F statistic.
State the relationships between convegence in a.s, p, r-th mean, d.
State the relationship between convergence in distribution and Op(1).
State and prove the relationship between convergence in distribution and Op(1).
Given the denominator from hypothesis testing, show another way to see convergence to q*sigma squared.
