Hellinger Deviance Tests: Efficiency, Breakdown Points, and Examples

References

• Beran , R. J. 1977 . “Minimum Hellinger Distance Estimates for Parametric Models,” . The Annals of Statistics , 5 : 445 – 463 .
   Web of Science ®Google Scholar
• Beran , R. J. 1981 . “Efficient Robust Tests in Parametric Models,” . Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete , 57 : 73 – 86 .
   Google Scholar
• Chernoff , H. 1954 . “On the Distribution of the Likelihood Ratio,” . The Annals of Mathematical Statistics , 25 : 573 – 578 .
   Google Scholar
• Cressie , N. and Read , T. 1984 . “Multinomial Goodness-of-Fit Tests,” . Journal of the Royal Statistical Society , 46 : 440 – 464 . Ser. B
   Google Scholar
• Devroye , L. and Gyorfi , L. 1985 . Nonparametric Density Estimation: The L₁ View , New York : John Wiley .
   Google Scholar
• Donoho , D. L. and Huber , P. J. 1983 . “The Notion of Breakdown Point,” . In A Festschrift for Erich L. Lehmann , Edited by: Bickel , P. , Doksum , K. and Hodges , J. L. Jr. 157 – 184 . Belmont , CA : Wadsworth .
   Google Scholar
• Donoho , D. L. and Liu , R. C. 1988 . “The ‘Automatic’ Robustness of Minimum Distance Functionals,” . The Annals of Statistics , 16 : 552 – 586 .
   Web of Science ®Google Scholar
• Fabian , V. and Hannan , J. 1985 . Introduction to Probability and Mathematical Statistics , New York : John Wiley .
   Google Scholar
• Freeman , M. F. and Tukey , J. W. 1950 . “Transformations Related to the Angular and the Square Root,” . The Annals of Mathematical Statistics , 21 : 607 – 611 .
   Google Scholar
• Hájek , J. and Šidák , Z. 1967 . Theory of Rank Tests , New York : Academic Press .
   Google Scholar
• Hampel , F. R. “Rejection Rules and Robust Estimates of Location: An Analysis of Some Monte Carlo Results,” . Transactions of the Seventh Prague Conference on Information Theory, Statistical Design Functions, Random Processes, and the 1974 European Meeting of Statisticians . Vol. A , pp. 187 – 194 . Dordrecht , , Holland : D. Reidel .
   Google Scholar
• Hampel , F. R. , Ronchetti , E. M. , Rousseeuw , P. J. and Stahel , W. A. 1986 . Robust Statistics: The Approach Based on Influence Functions , New York : John Wiley .
   Google Scholar
• He , X. , Simpson , D. G. and Portnoy , S. 1988 . “Refined Breakdown Analysis for Robust Tests,” , University of Illinois, Dept. of Statistics . Technical Report 9
   Google Scholar
• Ibragimov , I. A. and Has'minskii , R. Z. 1981 . Statistical Estimation: Asymptotic Theory , New York : Springer-Verlag .
   Google Scholar
• Knuth , D. E. 1969 . The Art of Computer Programming 2: Semi-numerical Algorithms , Reading , MA : Addison-Wesley .
   Google Scholar
• Kraft , C. 1955 . “Some Conditions for Consistency and Uniform Consistency of Statistical Procedures,” . University of California Publications in Statistics , 2 : 125 – 142 .
   Google Scholar
• Lambert , D. 1982 . “Qualitative Robustness of Tests,” . Journal of the American Statistical Association , 77 : 352 – 357 .
   Web of Science ®Google Scholar
• Matusita , K. 1955 . “Decision Rules, Based on the Distance, for Problems of Fit, Two Samples, and Estimation,” . The Annals of Mathematical Statistics , 26 : 631 – 640 .
   Google Scholar
• Neyman , J. and Pearson , E. S. 1928 . “On the Use and Interpretation of Certain Test Criteria for Purposes of Statistical Inference,” . Biometrika , 20 : 175 – 240 . Ser. A
   Google Scholar
• Rao , C. R. “Large Sample Tests of Statistical Hypotheses Concerning Several Parameters With Applications of Problems of Estimation,” . Proceedings of the Cambridge Philosophical Society . Vol. 44 , pp. 50 – 57 .
   Google Scholar
• Rao , C. R. 1973 . Linear Statistical Inference and Its Applications, , 2nd ed. , New York : John Wiley .
   Google Scholar
• Schrader , R. M. and Hettmansperger , T. P. 1980 . “Robust Analysis of Variance Based Upon a Likelihood Ratio Criterion,” . Biometrika , 67 : 93 – 101 .
   Web of Science ®Google Scholar
• Simpson , D. G. 1987 . “Minimum Hellinger Distance Estimation for the Analysis of Count Data,” . Journal of the American Statistical Association , 82 : 802 – 807 .
   Web of Science ®Google Scholar
• Simpson , D. G. , Carroll , R. J. and Ruppert , D. 1987 . “M-Estimation for Discrete Data: Asymptotic Distribution Theory and Implications,” . The Annals of Statistics , 15 : 657 – 669 .
   Web of Science ®Google Scholar
• Stather , C. R. 1981 . “Robust Statistical Inference Using Hellinger Distance Methods,” , LaTrobe University, Dept. of Mathematical Sciences . unpublished Ph.D. dissertation
   Google Scholar
• Tamura , R. and Boos , D. 1986 . “Minimum Hellinger Distance Estimation for Multivariate Location and Covariance,” . Journal of the American Statistical Association , 81 : 223 – 229 .
   Web of Science ®Google Scholar
• Wald , A. 1943 . “Tests of Statistical Hypotheses Concerning Several Parameters When the Number of Observations Is Large,” . Transactions of the American Mathematical Society , 54 : 426 – 482 .
   Google Scholar
• Welch , W. J. 1987 . “Rerandomizing the Median in Matched-Pairs Designs,” . Biometrika , 74 : 609 – 614 .
   Web of Science ®Google Scholar
• Wilks , S. S. 1938 . “The Large-Sample Distribution of the Likelihood Ratio for Testing Composite Hypothesis,” . The Annals of Mathematical Statistics , 9 : 60 – 62 .
   Google Scholar
• Woodruff , R. C. , Mason , J. M. , Valencia , R. and Zimmering , S. 1984 . “Chemical Mutagenesis Testing in Drosophila—I: Comparison of Positive and Negative Control Data for Sex-Linked Recessive Lethal Mutations and Reciprocal Translocations in Three Laboratories,” . Environmental Mutagenesis , 6 : 189 – 202 .
   PubMedGoogle Scholar
• Ylvisaker , D. 1977 . “Test Resistance,” . Journal of the American Statistical Association , 72 : 551 – 556 .
   Web of Science ®Google Scholar