STATS 300 A : Theory of Statistics Fall 2015 Lecture 3 —

STATS 300 A : Theory of Statistics Fall 2015 Lecture 14 — November 10

STATS 300 A : Theory of Statistics Fall 2015 Lecture 11 — October 27

This lemma allows us to find a minimax estimator for a particular tractable submodel, and then show that the worst-case risk for the full model is equal to that of the submodel (that is, the worst-case risk doesn’t rise as you go to the full model). In this case, using the Lemma, we can argue that the estimator we found is also minimax for the full model. This was similar to how we justified mi...

Stats 300 b : Theory of Statistics Winter 2017 Lecture 17 – March 7

STATS 300 A : Theory of Statistics Fall 2015 Lecture 10 — October 22

X1, . . . , Xn iid ∼ N (θ, σ), with σ known. Our goal is to estimate θ under squared-error loss. For our first guess, pick the natural estimator X. Note that it has constant risk σ 2 n , which suggests minimaxity because we know that Bayes estimators with constant risk are also minimax estimators. However, X is not Bayes for any prior, because under squared-error loss unbiased estimators are Ba...

Stats 300 b : Theory of Statistics Winter 2018 Lecture 15 – February 27

Theorem 1. Let {Xn}n=1 ⊂ L∞(T ) be a sequence of stochastic processes on T . The followings are equivalent. (1) Xn converge in distribution to a tight stochastic process X ∈ L∞(T ); (2) both of the followings: (a) Finite Dimensional Convergence (FIDI): for every k ∈ N and t1, · · · , tk ∈ T , (Xn(t1), · · · , Xn(tk)) converge in distribution as n→∞; (b) the sequence {Xn} is asymptotically stoch...