Lecture 11 Flashcards
Generally, what do we call Q_n? and what is theta_n in this context?
State the 3 conditions under which we can guarantee the consistency of theta.
Illustrate the importance of the compact set assumption in guaranteeing the consistency of theta hat.
State and prove that the 3 conditions we gave guarantee the consistency of theta hat.
State lemma 2: conditions that guarantee the sample mean of a function g(z_t,theta) converging in probability.
State and prove lemma 2: conditions that guarantee the sample mean of a function g(z_t,theta) converging in probability.
State the theorem regarding the convergence of a function g_n(theta) to a function g(theta).
State and prove the theorem regarding the convergence of a function g_n(theta) to a function g(theta) (overall).
In the proof of lemma 2: conditions that guarantee the sample mean of a function g(z_t,theta) converging in probability, state two conclusions regarding the compactness and continuity assumptions, and devise and upper bound for what we want to show.
Use the compactness assumption to split our expression into two parts starting with the expression, and show that the first term converges in the proof of lemma 2: conditions that guarantee the sample mean of a function g(z_t,theta) converging in probability,
State the the Lebesgue dominated convergence theorem.
In the proof of lemma 2: conditions that guarantee the sample mean of a function g(z_t,theta) converging in probability, show that the second term we are left with: converges.
