Lecture 4 Flashcards
State Theorem 13. Hint, relates eigenvalues to convergence.
Given a linear regression model with E[ui] = 0, E[ui*uj] = σ^2I(i = j)
Then the LSE estimator Bn converges in second mean to B iff the smallest eigenvalue of Z’Z goes to infinity.
What are two sufficient condition for an estimator to be consistent?
If E[Bn] = B and V(Bn) -> 0
Are the two conditions for sufficiency of consistency of an estimator necessary?
No, because consistency does not require any moments to be finite.
Given a stochastic Xn, define the notion that Xn = Op(fn).
If for all ε > 0, ∃ c >= 0 and n0 > 0 s.t
P{|Xn| > c*fn} < ε, for all n >= n0
Given a stochastic Xn, define the notion that Xn = op(fn).
If Xn/fn converges in probability to 0.
Describe the difference between Op(1) and op(1) withoout using the standard definitions.
Op(1) means P{|Xn| >c} < ε for some c > 0 while op(1) means for ALL c > 0.
What are the three components of Theorem 15? Hint: they link Op(f) to op(f) and the moments of Xn.S
Wat is Theorem 16? Hint: it links operations of variables to Op() and op().
State theorem 12
