## The Annals of Statistics

- Ann. Statist.
- Volume 5, Number 6 (1977), 1148-1169.

### Log-Linear Models and Frequency Tables with Small Expected Cell Counts

#### Abstract

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.

#### Article information

**Source**

Ann. Statist., Volume 5, Number 6 (1977), 1148-1169.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176344001

**Digital Object Identifier**

doi:10.1214/aos/1176344001

**Mathematical Reviews number (MathSciNet)**

MR448675

**Zentralblatt MATH identifier**

0404.62025

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62E20: Asymptotic distribution theory

Secondary: 62F05: Asymptotic properties of tests 62F10: Point estimation 62F25: Tolerance and confidence regions

**Keywords**

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

#### Citation

Haberman, Shelby J. Log-Linear Models and Frequency Tables with Small Expected Cell Counts. Ann. Statist. 5 (1977), no. 6, 1148--1169. doi:10.1214/aos/1176344001. https://projecteuclid.org/euclid.aos/1176344001