STAT330 Lecture Notes - The Algorithm, Logarithm, Likelihood Function

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

Document Summary

The the maximum likelihood (ml) estimate of , denoted by = (x1, . The corresponding ml estimator is = (x1, . The log-likelihood function is de ned as l( ) = log l( ), where log is the natural logarithmic function. The ml estimate of also maximizes l( ). Estimating ( ) the ml estimator of ( ) is just ( ). , xn are iid rvs from (a) poi( ) (b) exp( ) (try by yourself) (c) n( , 2) (d) unif(0, ), nd the ml estimator of in each case. Assume that is scalar in this section. Score function: the score function is de ned as. , xn) = d d l( ) = d d log l( ). If the support of f (x; ) does not depend on , then s( ) = 0. In this section, we consider how to solve s( ) = 0 numerically. Information function: the information function is de ned as.