Abstract.
The aim of this paper is to give some results on the exact density of the I-divergence in the exponential family with gamma distributed observations. It is shown in particular that the I-divergence can be decomposed as a sum of two independent variables with known distributions. Since the considered I-divergence is related to the likelihood ratio statistics, we apply the method to compute the exact distribution of the likelihood ratio tests and discuss the optimality of such exact tests. One of these tests is the exact LR test of the model which is asymptotically optimal in the Bahadur sense. Numerical examples are provided to illustrate the methods discussed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: January 2002
Acknowledgements. I am grateful to Prof. Andrej Pázman for helpful discussions during the setup and the preparation of the paper and to the referees for constructive comments on earlier versions of the paper.
Research is supported by the VEGA grant (Slovak Grant Agency) No 1/7295/20
Rights and permissions
About this article
Cite this article
Stehlík, M. Distributions of exact tests in the exponential family. Metrika 57, 145–164 (2003). https://doi.org/10.1007/s001840200206
Issue Date:
DOI: https://doi.org/10.1007/s001840200206