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A Note on Error Probabilities of the Likelihood Ratio Test Based on Transport Inequalities

  • Neng-Yi WangEmail author
  • Hui Jiang
Research article

Abstract

In this paper, by transport inequality theory, we obtain sharp and explicit upper bounds for any finite sample size \(n\ge 1\) on two types of error probabilities of the likelihood ratio tests about two-distribution hypotheses and one-sided parametric hypotheses.

Keywords

Error probability Likelihood ratio test Finite sample Transport inequality 

Mathematics Subject Classification

60E15 62F03 

Notes

Acknowledgements

The authors thank the referee and National Natural Science Foundation of China (No.11601170).

References

  1. Barron AR (1989) Uniformly powerful goodness of fit tests. Ann Stat 17:107–124MathSciNetCrossRefGoogle Scholar
  2. Berend D, Kontorovich A (2015) A finite-sample analysis of the naive Bayes classifier. J Mach Learn Res 16:1519–1545MathSciNetzbMATHGoogle Scholar
  3. Bolley F, Villani C (2005) Weighted Csisz\(\acute{a}\)r-Kullback-Pinsker inequalities and applications to transportation inequalities. Ann Fac Sci Toulouse Math (6) 14(3):331–352MathSciNetCrossRefGoogle Scholar
  4. Djellout H, Guillin A, Wu LM (2004) Transportation cost-information inequalities and application to random dynamical systems and diffusions. Ann. Probab 32(3B):2702–2732MathSciNetCrossRefGoogle Scholar
  5. Gozlan N, Léonard C (2007) A large deviation approach to some transportation cost inequalities. Probab Theory Relat Fields 139(1–2):235–283MathSciNetCrossRefGoogle Scholar
  6. Gozlan N, Léonard C (2010) Transport inequalities. A survey. Markov Process Relat Fields 16(4):635–736MathSciNetzbMATHGoogle Scholar
  7. Ledoux M (2001) The concentration of measure phenomenon. American Mathematical Society, ProvidencezbMATHGoogle Scholar
  8. Marton K (1996) Bounding d-distance by informational divergence: a method to prove measure concentration. Ann Probab 24(2):857–866MathSciNetCrossRefGoogle Scholar
  9. Ordentlich E, Weinberger Marcelo J (2005) A distribution dependent refinement of Pinsker’s inequality. IEEE Trans Inf Theory 51(5):1836–1840MathSciNetCrossRefGoogle Scholar
  10. Shao J (2003) Mathematical statistics. Springer texts in statistics, 2nd edn, xvi+591 pp. Springer, New York. ISBN: 0-387-95382-5 62-01CrossRefGoogle Scholar
  11. Wang NY (2014) Concentration inequalities for Gibbs sampling under \(d_{l_{2}}\)-metric. Electron Commun Probab 19(63):11zbMATHGoogle Scholar
  12. Wang NY, Wu L (2014) Convergence rate and concentration inequalities for Gibbs sampling in high dimension. Bernoulli 20(4):1698–1716MathSciNetCrossRefGoogle Scholar

Copyright information

© The Indian Society for Probability and Statistics (ISPS) 2019

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsHuazhong University of Science and TechnologyWuhanChina

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