Open Access
November, 1977 Log-Linear Models and Frequency Tables with Small Expected Cell Counts
Shelby J. Haberman
Ann. Statist. 5(6): 1148-1169 (November, 1977). DOI: 10.1214/aos/1176344001


In the case of frequency data, traditional discussions such as Rao (1973, pages 355-363, 391-412) consider asymptotic properties of maximum likelihood estimates and chi-square statistics under the assumption that all expected cell frequencies become large. If log-linear models are applied, these asymptotic properties may remain applicable if the sample size is large and the number of cells in the table is large, even if individual expected cell frequencies are small. Conditions are provided for asymptotic normality of linear functionals of maximum-likelihood estimates of log-mean vectors and for asymptotic chi-square distributions of Pearson and likelihood ratio chi-square statistics.


Download Citation

Shelby J. Haberman. "Log-Linear Models and Frequency Tables with Small Expected Cell Counts." Ann. Statist. 5 (6) 1148 - 1169, November, 1977.


Published: November, 1977
First available in Project Euclid: 12 April 2007

zbMATH: 0404.62025
MathSciNet: MR448675
Digital Object Identifier: 10.1214/aos/1176344001

Primary: 62E20
Secondary: 62F05 , 62F10 , 62F25

Keywords: asymptotic properties , chi-square tests , Contingency tables , log-linear models , maximum likelihood

Rights: Copyright © 1977 Institute of Mathematical Statistics

Vol.5 • No. 6 • November, 1977
Back to Top