STAT 450- Final Exam Guide - Comprehensive Notes for the exam ( 103 pages long!)

• School: University of Waterloo
• Department: Statistics
• Course: STAT450
• Professor: Liqun Diao

Document Summary

85 and therefore a 15% l. i. is an approximate 95% c. i. for . , xn) is a random sample from the distribution with prob- ability density function f (x; ) = x 1, The log likelihood and score function are l ( ) = n log + ( 1) > 0 npi=1 where t = log xi. S ( ) > 0 for 0 < < n/t and s ( ) < 0 for > n/t therefore by the first derivative test, = n/t is the m. l. estimate of . The m. l. estimator of is = n/t where t = log xi. npi=1. > 0 and the fisher information is. J ( ) = e [i ( ; x)] = e n. 1 n npi=1 log xi p e ( log xi; 0) = Maximum likelihood estimation and thus n is a consistent estimator of 0. 0 n 0 d z v n (0, 1) . (2. 8)