The Annals of Statistics

Log-Linear Models for Frequency Tables Derived by Indirect Observation: Maximum Likelihood Equations

Shelby J. Haberman

Full-text: Open access

Abstract

Frequency tables are examined in which some cells are not distinguishable. Log-linear models are proposed for these tables which lead to likelihood equations closely related to those associated with log-linear models for conventional frequency tables. Just as in conventional tables, the maximum likelihood equations are shown to be the same under Poisson or multinomial sampling. Applications are made to the problem of estimation of gene frequencies from observed phenotype frequencies.

Article information

Source
Ann. Statist., Volume 2, Number 5 (1974), 911-924.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176342813

Digital Object Identifier
doi:10.1214/aos/1176342813

Mathematical Reviews number (MathSciNet)
MR458687

Zentralblatt MATH identifier
0288.62013

JSTOR
links.jstor.org

Subjects
Primary: 62F10: Point estimation
Secondary: 62P10: Applications to biology and medical sciences

Keywords
Log-linear models contingency tables maximum likelihood estimation genetic models indirect observation

Citation

Haberman, Shelby J. Log-Linear Models for Frequency Tables Derived by Indirect Observation: Maximum Likelihood Equations. Ann. Statist. 2 (1974), no. 5, 911--924. doi:10.1214/aos/1176342813. https://projecteuclid.org/euclid.aos/1176342813


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