## The Annals of Statistics

### Higher-order asymptotic normality of approximations to the modified signed likelihood ratio statistic for regular models

#### Abstract

Approximations to the modified signed likelihood ratio statistic are asymptotically standard normal with error of order n−1, where n is the sample size. Proofs of this fact generally require that the sufficient statistic of the model be written as (θ̂, a), where θ̂ is the maximum likelihood estimator of the parameter θ of the model and a is an ancillary statistic. This condition is very difficult or impossible to verify for many models. However, calculation of the statistics themselves does not require this condition. The goal of this paper is to provide conditions under which these statistics are asymptotically normally distributed to order n−1 without making any assumption about the sufficient statistic of the model.

#### Article information

Source
Ann. Statist., Volume 35, Number 5 (2007), 2054-2074.

Dates
First available in Project Euclid: 7 November 2007

https://projecteuclid.org/euclid.aos/1194461722

Digital Object Identifier
doi:10.1214/009053607000000307

Mathematical Reviews number (MathSciNet)
MR2363963

Zentralblatt MATH identifier
1126.62013

Subjects
Primary: 62F05: Asymptotic properties of tests
Secondary: 62F03: Hypothesis testing

#### Citation

He, Heping; Severini, Thomas A. Higher-order asymptotic normality of approximations to the modified signed likelihood ratio statistic for regular models. Ann. Statist. 35 (2007), no. 5, 2054--2074. doi:10.1214/009053607000000307. https://projecteuclid.org/euclid.aos/1194461722

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