Date of Award


Document Type

Master's report

Degree Name

Master of Science in Mathematical Sciences (MS)

College, School or Department Name

Department of Mathematical Sciences


Iosif Pinelis


This report reviews literature on the rate of convergence of maximum likelihood estimators and establishes a Central Limit Theorem, which yields an O(1/sqrt(n)) rate of convergence of the maximum likelihood estimator under somewhat relaxed smoothness conditions. These conditions include the existence of a one-sided derivative in θ of the pdf, compared to up to three that are classically required. A verification through simulation is included in the end of the report.