The Annals of Statistics

A large deviation theorem for the q-sample likelihood ratio statistic

František Rublík

Full-text: Open access

Abstract

An upper bound for the tail probability $P_{\theta} (\log (L(x_{(n_1, \dots, n_q)}, \Theta)/L(x_{(n_1, \dots, n_q)}, \theta)) \geq t)$ is derived in the case of sampling from q populations. This estimate is used for establishing the Hodges-Lehmann optimality of a test statistic for a hypothesis on exponential distributions.

Article information

Source
Ann. Statist., Volume 24, Number 5 (1996), 2280-2287.

Dates
First available in Project Euclid: 20 November 2003

Permanent link to this document
https://projecteuclid.org/euclid.aos/1069362322

Digital Object Identifier
doi:10.1214/aos/1069362322

Mathematical Reviews number (MathSciNet)
MR1421173

Zentralblatt MATH identifier
0867.62008

Subjects
Primary: 60F10: Large deviations 62F05: Asymptotic properties of tests
Secondary: 62E15: Exact distribution theory 62F12: Asymptotic properties of estimators

Keywords
Large deviations exponential distributions with unknown lower bound Hodges-Lehmann optimality

Citation

Rublík, František. A large deviation theorem for the q -sample likelihood ratio statistic. Ann. Statist. 24 (1996), no. 5, 2280--2287. doi:10.1214/aos/1069362322. https://projecteuclid.org/euclid.aos/1069362322


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