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

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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.

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References

  • Barron AR (1989) Uniformly powerful goodness of fit tests. Ann Stat 17:107–124

    Article  MathSciNet  Google Scholar 

  • Berend D, Kontorovich A (2015) A finite-sample analysis of the naive Bayes classifier. J Mach Learn Res 16:1519–1545

    MathSciNet  MATH  Google Scholar 

  • 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):331–352

    Article  MathSciNet  Google Scholar 

  • Djellout H, Guillin A, Wu LM (2004) Transportation cost-information inequalities and application to random dynamical systems and diffusions. Ann. Probab 32(3B):2702–2732

    Article  MathSciNet  Google Scholar 

  • Gozlan N, Léonard C (2007) A large deviation approach to some transportation cost inequalities. Probab Theory Relat Fields 139(1–2):235–283

    Article  MathSciNet  Google Scholar 

  • Gozlan N, Léonard C (2010) Transport inequalities. A survey. Markov Process Relat Fields 16(4):635–736

    MathSciNet  MATH  Google Scholar 

  • Ledoux M (2001) The concentration of measure phenomenon. American Mathematical Society, Providence

    MATH  Google Scholar 

  • Marton K (1996) Bounding d-distance by informational divergence: a method to prove measure concentration. Ann Probab 24(2):857–866

    Article  MathSciNet  Google Scholar 

  • Ordentlich E, Weinberger Marcelo J (2005) A distribution dependent refinement of Pinsker’s inequality. IEEE Trans Inf Theory 51(5):1836–1840

    Article  MathSciNet  Google Scholar 

  • Shao J (2003) Mathematical statistics. Springer texts in statistics, 2nd edn, xvi+591 pp. Springer, New York. ISBN: 0-387-95382-5 62-01

    Book  Google Scholar 

  • Wang NY (2014) Concentration inequalities for Gibbs sampling under \(d_{l_{2}}\)-metric. Electron Commun Probab 19(63):11

    MATH  Google Scholar 

  • Wang NY, Wu L (2014) Convergence rate and concentration inequalities for Gibbs sampling in high dimension. Bernoulli 20(4):1698–1716

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

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

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Authors and Affiliations

  1. School of Mathematics and Statistics, Huazhong University of Science and Technology, Luoyu Road 1037, Hongshan District, Wuhan, 430074, China

    Neng-Yi Wang & Hui Jiang

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  1. Neng-Yi Wang
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  2. Hui Jiang
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Correspondence to Neng-Yi Wang.

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Wang, NY., Jiang, H. A Note on Error Probabilities of the Likelihood Ratio Test Based on Transport Inequalities. J Indian Soc Probab Stat 20, 201–225 (2019). https://doi.org/10.1007/s41096-019-00064-9

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  • DOI: https://doi.org/10.1007/s41096-019-00064-9

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