Open Access
April 2020 Bounds for the asymptotic distribution of the likelihood ratio
Andreas Anastasiou, Gesine Reinert
Ann. Appl. Probab. 30(2): 608-643 (April 2020). DOI: 10.1214/19-AAP1510


In this paper, we give an explicit bound on the distance to chi-square for the likelihood ratio statistic when the data are realisations of independent and identically distributed random elements. To our knowledge, this is the first explicit bound which is available in the literature. The bound depends on the number of samples as well as on the dimension of the parameter space. We illustrate the bound with three examples: samples from an exponential distribution, samples from a normal distribution and logistic regression.


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Andreas Anastasiou. Gesine Reinert. "Bounds for the asymptotic distribution of the likelihood ratio." Ann. Appl. Probab. 30 (2) 608 - 643, April 2020.


Received: 1 August 2018; Revised: 1 May 2019; Published: April 2020
First available in Project Euclid: 8 June 2020

zbMATH: 07236129
MathSciNet: MR4108117
Digital Object Identifier: 10.1214/19-AAP1510

Primary: 62E17 , 62H15
Secondary: 60F05

Keywords: Log-likelihood ratio statistics , Stein’s method , Wilks’ theorem

Rights: Copyright © 2020 Institute of Mathematical Statistics

Vol.30 • No. 2 • April 2020
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