A Cornucopia of Maximum Likelihood Algorithms

Kenneth Lange, Xun-Jian Li and Hua Zhou

The American Statistician, 2025, vol. 79, issue 4, 538-548

Abstract: Classroom expositions of maximum likelihood estimation (MLE) rely on traditional calculus methods to construct analytic solutions. This creates in students a false sense of the ease with which MLE problems can be attacked. In a nod to reality, some teachers mention and apply Newton’s method, Fisher scoring, and the expectation-maximization (EM) algorithm. Although preferable to leaving students in a state of ignorance, such brief expositions ultimately fail to expose the full body of relevant techniques. Some of these techniques extend more readily to high-dimensional data problems than Newton’s method and scoring. The current paper emphasizes block ascent and descent, profile likelihoods, the minorization-maximization (MM) principle, and their creative combination. These themes are put to work in readable Julia code to solve several MLE problems.

Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/00031305.2025.2526535 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:amstat:v:79:y:2025:i:4:p:538-548

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/UTAS20

DOI: 10.1080/00031305.2025.2526535

Access Statistics for this article

The American Statistician is currently edited by Eric Sampson

More articles in The American Statistician from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().