On Neyman-Pearson Principle in Multiple Hypotheses Testing


  • Evgueni A. Haroutunian Institute for Informatics and Automation Problems of NAS RA
  • Parandzem M. Hakobyan Institute for Informatics and Automation Problems of NAS RA


Multiple hypotheses, Optimal statistical test, Error probability, Neyman-Pearson Lemma


The aim of this paper is to newly generalize the classical Neyman-Pearson Lemma to the case of more than two simple hypotheses.


J. Neyman and E.S. Pearson, “On the problem of the most efficient tests of statistical hypotheses", Phil. Trans. Roy. Soc. London, Ser. A, 231, pp. 289-337, 1933.

J. Neyman, First Course in Probability and Statistics, Holt, Rinehart and Winston, New York, 1950.

E.L. Lehman and J.P. Romano, Testing statistical hypotheses, Third Edition. Springer, New York, 2005.

A.A. Borovkov, Mathematical Statistics, in Russian, Nauka, Moscow, 1997.

H.L. Van Trees, Detection, Estimation and Modulation Theory, Part 1. New York: Wiley, 1968.

M.H. DeGroot, Probability and Statistics, 2nd ed., Reading, MA, Addison-Wesley, 1986.

M.G. Kendall and A. Stuart, The Advanced Theory of Statistics, 2, Inference and relationship, Third edition. Hafner publishing company, London, 1961.

A.K. Bera, “Hypothesis testing in the 20-th century with a special reference to testing with misspecified models", In: “Statistics for the 21-st century. Methodologies for applications of the Fitire", Marcel Dekker, Inc., New York, Basel, pp. 33-92, 2000.

I. Csisz¶ar and J. KÄorner, Information Theory: Coding Theorems for Discrete Memoryless Systems, Academic Press, New York, 1981, (Russian translation, Mir, Muscow, 1985)

T.M. Cover and J.A. Thomas, Elements of Information Theory, Second Edition. Wiley, New York, 2006.

E. Levitan and N. Merhav, “A competitive Neyman-Pearson approach to universal hypothesis testing with applications", IEEE Transactions on Information Theory, vol. 48, no. 8, pp. 2215-2229, 2002.

P. Moulin, “A Neyman-Pearson approach to universal erasure and list decoding", ISIT, Toronto, Canada, July 6-11, 2008.

P.-N. Chen, “General formulas for the Neyman-Pearson type-II error exponent subject to fixed and exponential type-I error bounds", IEEE Transactions on Information Theory, vol. 42, no. 1 , pp. 316-323, 1996.

C.C. Leang and D.H. Johnson, “On the asymptotics of M-hypothesis Bayesian detection", IEEE Transactions on Information Theory, vol. 43, no. 1, pp. 280-282, 1997.

E.A. Haroutunian, “Neyman-Pearson principle for more than two hypotheses", Abstracts of Armenian Mathematical Union Annual Session Dedicated to 90 Anniversary of Rafael Alexandrian, Yerevan, pp.49-50, 2013.




How to Cite

Haroutunian, E. A., & Hakobyan, P. M. (2021). On Neyman-Pearson Principle in Multiple Hypotheses Testing. Mathematical Problems of Computer Science, 40, 34–38. Retrieved from http://mpcs.sci.am/index.php/mpcs/article/view/307

Most read articles by the same author(s)

1 2 > >>