## The Annals of Statistics

### Stochastic Inequalities Relating a Class of Log-Likelihood Ratio Statistics to their Asymptotic $\chi^2$ Distribution

B. T. Porteous

#### Abstract

For decomposable covariance selection models, stochastic inequalities which relate the null distribution of the log-likelihood ratio statistic to its asymptotic $\chi^2$ distribution are obtained. The implications are twofold: First, the null distribution of the log-likelihood ratio statistic is seen to be stochastically larger than its asymptotic $\chi^2$ distribution. Extremely large samples apart, for the $\chi^2$ approximation to be valid, a deflation of the log-likelihood ratio statistic is then necessary. Second, a simple adjustment to the log-likelihood ratio statistic, similar in spirit to the Bartlett adjustment, yields a conservative test.

#### Article information

Source
Ann. Statist., Volume 17, Number 4 (1989), 1723-1734.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176347390

Digital Object Identifier
doi:10.1214/aos/1176347390

Mathematical Reviews number (MathSciNet)
MR1026308

Zentralblatt MATH identifier
0694.62010

JSTOR
Porteous, B. T. Stochastic Inequalities Relating a Class of Log-Likelihood Ratio Statistics to their Asymptotic $\chi^2$ Distribution. Ann. Statist. 17 (1989), no. 4, 1723--1734. doi:10.1214/aos/1176347390. https://projecteuclid.org/euclid.aos/1176347390