## The Annals of Statistics

### Standardized Log-Likelihood Ratio Statistics for Mixtures of Discrete and Continuous Observations

J. L. Jensen

#### Abstract

When the $\log$-likelihood statistic is divided by its mean, or an approximation to its mean, the limiting chi-squared distribution is often correct to order $n^{-3/2}$. Similarly, when the signed version of the likelihood ratio statistic is standardized with respect to its mean and variance the normal approximation is correct to order $n^{-3/2}$. Proofs for these statements have been given in great generality in the literature for the case of continuous observations. In this paper we consider cases where the minimal sufficient statistic is partly discrete and partly continuous. In particular, we consider testing problems associated with censored exponential life times.

#### Article information

Source
Ann. Statist., Volume 15, Number 1 (1987), 314-324.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176350268

Digital Object Identifier
doi:10.1214/aos/1176350268

Mathematical Reviews number (MathSciNet)
MR885739

Zentralblatt MATH identifier
0613.62014

JSTOR