## The Annals of Statistics

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

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

#### 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**

links.jstor.org

**Subjects**

Primary: 62E20: Asymptotic distribution theory

Secondary: 62F05: Asymptotic properties of tests

**Keywords**

Censored life times conditional expansion transformed expansion

#### Citation

Jensen, J. L. Standardized Log-Likelihood Ratio Statistics for Mixtures of Discrete and Continuous Observations. Ann. Statist. 15 (1987), no. 1, 314--324. doi:10.1214/aos/1176350268. https://projecteuclid.org/euclid.aos/1176350268