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About: Maximum Likelihood Estimation

Module by: Clayton Scott, Robert Nowak. E-mail the authors

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Name: Maximum Likelihood Estimation
ID: m11446
Language: English (en)
Summary: This module introduces the maximum likelihood estimator. We show how the MLE implements the likelihood principle. Methods for computing th MLE are covered. Properties of the MLE are discussed including asymptotic efficiency and invariance under reparameterization.
Subject: Mathematics and Statistics, Science and Technology
Keywords: Fisher information, invariance, likelihood function, likelihood principle, Maximum Likelihood Estimation, Maximum Likelihood Estimators, MLE
Document Type: -//CNX//DTD CNXML 0.5 plus MathML//EN
License: Creative Commons Attribution License CC-BY 1.0

Authors: Clayton Scott (, Robert Nowak (
Copyright Holders: Clayton Scott (, Robert Nowak (
Maintainers: Clayton Scott (, Robert Nowak (, Elizabeth Gregory (, Jeffrey Silverman (

Latest version: 1.5 (history)
First publication date: Jul 9, 2003 2:30 pm +0000
Last revision to module: May 12, 2004 11:50 am +0000


PDF: m11446_1.5.pdf PDF file, for viewing content offline and printing. Learn more.
XML: m11446_1.5.cnxml XML that defines the structure and contents of the module, minus any included media files. Can be reimported in the editing interface. Learn more.

Version History

Version: 1.5 May 12, 2004 11:50 am +0000 by Jeffrey Silverman
Fixed PDFs and a couple typos.

Version: 1.4 Oct 31, 2003 3:05 pm +0000 by Clayton Scott
Significantly reworked the organization of Rob's version, added lots of commentary, and left some math for Jeff to type in.

Version: 1.3 Oct 24, 2003 4:49 pm +0000 by Clayton Scott
Major overhaul: Rearranged a bunch of stuff, deleted some stuff, added a lot of commentary, and left some LaTeX math for Jeff to covert to MathML.

Version: 1.2 Aug 7, 2003 2:53 pm +0000 by Jeffrey Silverman
Added Clay as an author and maintainer.

Version: 1.1 Jul 14, 2003 4:42 pm +0000 by Elizabeth Gregory
First Version

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American Chemical Society (ACS) Style Guide:

Scott, C.; Nowak, R. Maximum Likelihood Estimation, OpenStax-CNX Web site., May 12, 2004.

American Medical Assocation (AMA) Manual of Style:

Scott C, Nowak R. Maximum Likelihood Estimation [OpenStax-CNX Web site]. May 12, 2004. Available at:

American Psychological Assocation (APA) Publication Manual:

Scott, C., & Nowak, R. (2004, May 12). Maximum Likelihood Estimation. Retrieved from the OpenStax-CNX Web site:

Chicago Manual of Style (Bibliography):

Scott, Clayton, and Robert Nowak. "Maximum Likelihood Estimation." OpenStax-CNX. May 12, 2004.

Chicago Manual of Style (Note):

Clayton Scott and Robert Nowak, "Maximum Likelihood Estimation," OpenStax-CNX, May 12, 2004,

Chicago Manual of Style (Reference, in Author-Date style):

Scott, C., & Nowak, R. 2004. Maximum Likelihood Estimation. OpenStax-CNX, May 12, 2004.

Modern Languages Association (MLA) Style Manual:

Scott, Clayton, and Robert Nowak. Maximum Likelihood Estimation. OpenStax-CNX. 12 May 2004 <>.