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Theory and Methods

Statistical Inference Based on Pseudo-Maximum Likelihood Estimators in Elliptical Populations

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Pages 135-143 | Published online: 20 Dec 2012

REFERENCES

  • Aitchison , J. and Silvey , S. D. 1958 . “Maximum Likelihood Estimation of Parameters Subject to Restraints,” . Annals of Mathematical Statistics , 29 : 813 – 828 .
  • Amemiya , T. 1985 . Advanced Econometrics Cambridge , MA : Harvard University Press. .
  • Bentler , P. M. 1983 . “Some Contributions to Efficient Statistics in Structural Models: Specification and Estimation of Moment Structures,” . Psychometrika , 48 : 493 – 517 .
  • Berkane , M. and Bentler , P. M. 1986 . “Moments of Elliptically Distributed Random Variates,” . Statistics and Probability Letters , 4 : 333 – 335 .
  • Berkane , M. and Bentler , P. M. 1987 . “Characterizing Parameters of Multivariate Elliptical Distributions,” . Communications in Statistics, Part B—Simulation and Computation , 16 : 193 – 198 .
  • Berkane , M. and Bentler , P. M. 1988 . “Estimation of Contamination Parameters and Identification of Outliers in Multivariate Data,” . Sociological Methods and Research , 17 : 55 – 64 .
  • Berkane , M. , Kano , Y. and Bentler , P. M. 1992 . “Pseudo-Maximum Likelihood Estimation in Elliptical Theory: Effects of Misspecification,” submitted
  • Bickel , P. J. 1982 . “On Adaptive Estimation,” . The Annals of Statistics , 10 : 647 – 671 .
  • Browne , M. W. 1974 . “Generalized Least Squares Estimators in the Analysis of Covariance Structures,” . South African Statistical Journal , 8 : 1 – 24 .
  • Browne , M. W. 1982 . “Covariance Structures,”. ” . In Topics in Applied Multivariate Analysis Edited by: Hawkins , D. M. 72 – 141 . Cambridge , , U.K. : Cambridge University Press. .
  • Browne , M. W. 1984 . “Asymptotically Distribution-Free Methods for the Analysis of Covariance Structures” . British Journal of Mathematical and Statistical Psychology , 37 : 62 – 83 .
  • Buse , A. 1982 . “The Likelihood Ratio, Wald, and Lagrange Multiplier Tests: An Expository Note,” . The American Statistician , 36 : 153 – 157 .
  • Davidson , R. R. and Lever , W. E. 1970 . “The Limiting Distribution of the Likelihood Ratio Statistic Under a Class of Local Alternatives,” . Sankhyâ , 32 : 209 – 224 . Ser. A
  • Dempster , A. P. , Laird , N. M. and Rubin , D. B. 1977 . “Maximum Likelihood From Incomplete Data Via the EM Algorithm,” . Journal of the Royal Statistical Society , 39 : 1 – 38 . Ser. B
  • Foutz , R. V. and Srivastava , R. C. 1977 . “The Performance of the Likelihood Ratio Test When the Model is Incorrect,” . The Annals of Statistics , 5 : 1183 – 1194 .
  • Gong , G. and Samaniego , F. J. 1981 . “Pseud—Maximum Likelihood Estimation: Theory and Applications,” . The Annals of Statistics , 9 : 861 – 869 .
  • 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. .
  • Huber , P. “The Behavior of Maximum Likelihood Estimates Under Nonstandard Conditions,” . Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability . pp. 221 – 233 . Berkeley , CA : University of California Press. .
  • Huber , P. 1981 . Robust Statistics New York : John Wiley. .
  • Kano , Y. 1986 . “Conditions on Consistency of Estimators in Covariance Structure Model,” . Journal of the Japan Statistical Society , 16 : 75 – 80 .
  • Kelker , D. 1970 . “Distribution Theory of Spherical Distributions and a Location-Scale Parameter,” . Sankhyâ , 32 : 419 – 430 . Ser. A
  • Kent , J. T. 1982 . “Robust Properties of Likelihood Ratio Tests,” . Biometrika , 69 : 19 – 27 .
  • Lange , K. L. , Little , R. J. A. and Taylor , J. M. G. 1989 . “Robust Statistical Modeling Using the T Distribution,” . Journal of the American Statistical Association , 84 : 881 – 896 .
  • Lee , S.-Y. and Bentler , P. M. 1980 . “Some Asymptotic Properties of Constrained Generalized Least Squares Estimation in Covariance Structure Models,” . South African Statistical Journal , 14 : 121 – 136 .
  • Lehmann , E. L. 1983 . Theory of Point Estimation New York : John Wiley. .
  • Little , R. J. A. 1988 . “Robust Estimation of the Mean and Covariance Matrix From Data With Missing Values,” . Applied Statistics , 37 : 23 – 38 .
  • Mardia , K. V. 1970 . “Measures of Multivariate Skewness and Kurtosis With Applications,” . Biometrika , 57 : 519 – 530 .
  • Maronna , R. A. 1976 . “Robust M Estimators of Multivariate Location and Scatter,” . The Annals of Statistics , 4 : 51 – 67 .
  • Mitchell , A. F. S. 1989 . “The Information Matrix, Skewness Tensor, and α Connection for the General Multivariate Elliptic Distribution,” . The Annals of the Institute of Statistical Mathematics , 41 : 289 – 304 .
  • Muirhead , R. J. 1982 . Aspects of Multivariate Statistical Theory New York : John Wiley. .
  • Muirhead , R. J. and Waternaux , C. M. 1980 . “Asymptotic Distributions in Canonical Correlation Analysis and Other Multivariate Procedures for Nonnormal Populations,” . Biometrika , 67 : 31 – 43 .
  • Nel , D. G. 1980 . “On Matrix Differentiation in Statistics,” . South African Statistical Journal , 14 : 137 – 193 .
  • Nishii , R. 1988 . “Maximum Likelihood Principle and Model Selection When the True Model is Unspecified,” . Journal of Multivariate Analysis , 27 : 392 – 403 .
  • Parke , W. R. 1986 . “Pseudo-Maximum Likelihood Estimation: The Asymptotic Distribution,” . The Annals of Statistics , 14 : 355 – 357 .
  • Ranga Rao , R. 1962 . “Relations Between Weak and Uniform Convergence of Measures With Applications,” . Annals of Mathematical Statistics , 33 : 659 – 680 .
  • Rao , C. R. 1947 . “Large Sample Tests of Statistical Hypotheses Concerning Several Parameters With Applications to Problems of Estimation,” . Proceedings of the Cambridge Philosophical Society , 44 : 50 – 57 .
  • Rao , C. R. 1973 . Linear Statistical Inference and Its Applications, , 2nd ed. New York : John Wiley. .
  • Romano , J. P. and Siegel , A. F. 1986 . Counterexamples in Probability and Statistics Monterey , CA : Wadsworth and Brooks/Cole. .
  • Satorra , A. 1989 . “Alternative Test Criteria in Covariance Structure Analysis: A Unified Approach,” . Psychometrika , 54 : 131 – 151 .
  • Shapiro , A. and Browne , M. W. 1987 . “Analysis of Covariance Structures Under Elliptical Distributions,” . Journal of the American Statistical Association , 82 : 1092 – 1097 .
  • Taylor , J. M. G. 1992 . “Properties of Modelling the Error Distribution With an Extra Shape Parameter,” . Computational Statistics & Data Analysis , 13 : 33 – 46 .
  • Tyler , D. E. 1982 . “Radial Estimates and the Test for Sphericity,” . Biometrika , 69 : 429 – 436 .
  • Tyler , D. E. 1983 . “Robustness and Efficiency Properties of Scatter Matrices,” . Biometrika , 70 : 411 – 420 .
  • Tyler , D. E. 1987 . “A Distribution-Free M Estimator of Multivariate Scatter,” . The Annals of Statistics , 15 : 234 – 251 .
  • 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 .
  • White , H. 1981 . “Consequences and Detection of Misspecified Nonlinear Regression Models,” . Journal of the American Statistical Association , 76 : 419 – 433 .
  • White , H. 1982 . “Maximum Likelihood Estimation of Misspecified Models,” . Econometrica , 50 : 1 – 25 .
  • Yamaguchi , K. “Generalized EM Algorithm for Models With Contaminated Error Terms,” . Proceedings of the Seventh Japan and Korea Joint Conference of Statistics . pp. 107 – 114 .

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