STAT330 Lecture Notes - Independent And Identically Distributed Random Variables, Delta Method

• School: University of Waterloo
• Department: Statistics
• Course: STAT330
• Professor: Christine Dupont

Document Summary

A review of "convergence in distribution to a degenerate r. v. " examples, with a focus on discontinuity points e. g. 1) yn = max(x1, . Step 2: n p (yn y) = lim. Note the point of discontinuity at y = 1: check p (yn 1) = 1n = 1 1 as n . e. g. 2) yn = min(x1, . Note the point of discontinuity at y = 0: check p (yn 0) = 1 [1 0]n = 1 1n = 1 1 = 0 0 as n . e. g. 3) (example 5. 2. 5 revisited) yn = max(x1, . And f (x) = 0, x . Find the limiting distribution of yn. iid f (x) = 1 e (x ), x > Step 2: n p (yn y) = lim (cid:40) Note the point of discontinuity at y = : check p (yn ) = 1 e n( ) = 1 e0 = 1 1 0 as n .