On d -optimality of the LR tests

František Rublík

Kybernetika (1995)

  • Volume: 31, Issue: 2, page 189-206
  • ISSN: 0023-5954

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Rublík, František. "On $d$-optimality of the LR tests." Kybernetika 31.2 (1995): 189-206. <http://eudml.org/doc/27581>.

@article{Rublík1995,
author = {Rublík, František},
journal = {Kybernetika},
keywords = {multinomial distribution; normal distribution; testing sphericity of covariance matrices; testing independence; contingency tables; testing equality of means; lower asymptotic distributional bound; likelihood ratio statistics; regularity conditions; multinomial; Poisson distribution},
language = {eng},
number = {2},
pages = {189-206},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On $d$-optimality of the LR tests},
url = {http://eudml.org/doc/27581},
volume = {31},
year = {1995},
}

TY - JOUR
AU - Rublík, František
TI - On $d$-optimality of the LR tests
JO - Kybernetika
PY - 1995
PB - Institute of Information Theory and Automation AS CR
VL - 31
IS - 2
SP - 189
EP - 206
LA - eng
KW - multinomial distribution; normal distribution; testing sphericity of covariance matrices; testing independence; contingency tables; testing equality of means; lower asymptotic distributional bound; likelihood ratio statistics; regularity conditions; multinomial; Poisson distribution
UR - http://eudml.org/doc/27581
ER -

References

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  1. R. R. Bahadur T. K. Chandra, D. Lambert, Some further properties of likelihood ratios on general sample spaces, In: Proceedings of the Indian Statistical Institute Golden Jubilee International Conference on Statistics: Applications and New Directions, 1981. (1981) MR0786130
  2. R. H. Berk, Consistency and asymptotic normality of mle's for exponential models, Ann. Math. Statist. 43 (1972), 193-204. (1972) Zbl0253.62005MR0298810
  3. R. H. Berk, Stochastic bounds for attained levels, J. Multivariate Anal. 14 (1984), 376-389. (1984) Zbl0573.62023MR0747265
  4. H. Cramer, Mathematical Methods of Statistics, Princeton University Press, Princeton 1946. (1946) Zbl0063.01014MR0016588
  5. D. G. Herr, Asymptotically optimal tests for multivariate normal distributions, Ann. Math. Statist. 38 (1967), 1829-1844. (1967) Zbl0153.47801MR0223004
  6. W. Hoeffding, Asymptotically optimal tests for multinomial distributions, Ann. Math. Statist. 36 (1965), 369-408. (1965) Zbl0135.19706MR0173322
  7. S. Kourouklis, Hodges-Lehmann optimality of the likelihood ratio test in regular exponential families of distributions, Technical Report 73. The Pennsylvania State University, Dept. of Statistics, 1987. (1987) 
  8. A. M. Kshirsagar, Multivariate Analysis, Marcel Dekker, New York 1972. (1972) Zbl0246.62064MR0343478
  9. E. L. Lehmann, Testing Statistical Hypotheses, Wiley, New York 1959. (1959) Zbl0089.14102MR0107933
  10. F. Rublík, On optimality of the LR tests in the sense of exact slopes. Part II. Application to individual distributions, Kybernetika 25(1989), 117-135. (1989) MR0995954
  11. F. Rublík, On consistency of the MLE, Kybernetika 31 (1995), 45-64. (1995) MR1324660
  12. M. S. Srivastava, C. G. Khatri, An Introduction to Multivariate Statistics, North Holland, New York 1979. (1979) Zbl0421.62034MR0544670

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