On Bahadur Efficiency and Bartlett Adjustability of Quasi-LRT Statistics

  • Published : 1998.09.01

Abstract

When the LRT is not feasible, we define quasi-LRT(QLRT) as a modification of the LRT Under some appropriate conditions the QLRT shares Bahadur optimality and Bartlett Adjustability with the LRT. When we can find maximum likelihood estimator under the null parameter space but not under the unrestricted parameter space, our QLRT is Bahadur optimal as is the LRT We suggest the stopping rule of the Newton-Raphson iterations for constructing the QLRT statistics which are Bartlett adjustable.

Keywords

References

  1. Annals of Mathematical Statistics v.31 Stochastic comparison of tests Bahadur, R. R.
  2. Sankya v.22 Asymptotic effuciency of tests and estimates Bahadur, R. R.
  3. Proceeding of Fifth Berkeley Symposium in Mathematical Statistics and Problability An optimal property of the likelihood ratio statistic Bahadur, R. R.
  4. Annals of Mathematical Statistics v.38 Rate of comvergence of estimates and test statistics Bahadur, R. R.
  5. Society for Industrial ans Applied Mathematics Somu limits theorems in Satistics Bahadur,R. R.
  6. Proceeding of Sixth Berkeley Sumposium in Mathematical Statistics and Probaility Some asymptotic properties of liklihood ratios and general sample space Bahadur, R. R.;Raghavachari, M.
  7. Journal of Doyal Ststistical society, Series B v.41 Bartlett adjustments to the likelihood ratio statistic and the distribution of the maximum likelihood estimator Barndorff-Nielsen, O. E.;Cox, D. R.
  8. Biometrika v.75 On the level-error after Bartlett asjudtment of the likelihood ratio statistic Barndorff-Nielsen, O. E.;Hall, P.
  9. Journal of Multivariate Analysis v.14 Stochastic bounds for attained levels Berk, R. H.
  10. Biometrika v.62 The likelihood ratio criterion for a composite hypothesis under a local alternative Hayakawa, T.
  11. Annals of Institute of Mathematical Statistics v.29 The likelihood ratio criterion and the asympotic expansion of its distribution Hayakawa, T.
  12. Biometrika v.43 A general method for approximating to the distribution of likelihood ratio criteria Lawley, D. N.
  13. Unpublished Ph. D dissertation at Rutges University Lee, K. J.
  14. Annals of Mathematical Statistics v.41 On a theorem of Bahadur on the rate of convergence of test statistics Raghavachari, M.
  15. Annals of Mathematical Ststistics v.9 The large-sample distribution of the likelihood ratio for testing composite hypothesis Wilks, S. S.