Stat 418 – Day 3 Maximum Likelihood Estimation (Ch. 1)

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Presentation transcript:

Stat 418 – Day 3 Maximum Likelihood Estimation (Ch. 1)

Last Time Multiple confidence interval procedures for   Main goal: Achieve stated confidence level, e.g., 95% of intervals for all possible random samples capture the value of the parameter  Also nice if narrower

Confidence interval for  Exact binomial Wald interval Score interval (Wilson)  Which values of  would not be rejected… Adjusted Wald (Agresti & Coull, 1998)  Approximate is better than "exact" for interval estimation of binomial proportions, American Statistician, 52:119–126.

Likelihood function =C(407,248)  248 (1-  ) 209

Test of significance? Gives you a point estimate Also allows you to compare to other values  Another value of  will be plausible if the likelihood function at that value isn’t too much smaller

Likelihood ratio test Likelihood Ratio compares the unrestricted maximum likelihood to value under null Pearson is z 2 from “score” test (two-sided)

To Do Finish reading Ch. 1 Investigation 1 HW 1 solutions posted tonight? HW 2 posted this weekend? Final Exam survey (by Monday?)