Normal/Independent Distributions and Their Applications in Robust Regression

References

• Andrews , D. F. and Mallows , C. L. 1974 . “Scale Mixtures of Normal Distributions” . Journal of the Royal Statistical Society , 36 : 99 – 102 . Ser. B
   Google Scholar
• Berk , R. A. 1989 . “A Primer on Robust Regression” . UCLA Statistics Series , 12 : 1 – 42 .
   Google Scholar
• Billingsley , P. 1986 . Probability and Measure, , 2nd ed. , New York : John Wiley .
   Google Scholar
• Böhning , D. and Lindsay , B. G. 1988 . “Monotonicity of Quadratic Approximation Algorithms” . Annals of the Institute of Statistical Mathematics , 40 : 641 – 663 .
   Web of Science ®Google Scholar
• Box , G. E. P. and Tiao , G. C. 1973 . Bayesian Inference in Statistical Analysis , Reading , MA : Addison-Wesley .
   Google Scholar
• Cornish , E. A. 1954 . “The Multivariate t Distribution Associated With a Set of Normal Standard Deviates” . Australian Journal of Physics , 7 : 531 – 542 .
   Google Scholar
• Crone , C. 1963 . “The Permeability of Capillaries in Various Organs as Determined By the Indicator Diffusion Method” . Acta Physiologica Scandinavica , 58 : 292 – 305 .
   PubMedGoogle Scholar
• Dempster , A. P. , Laird , N. M. and Rubin , D. B. 1977 . “Maximum Likelihood Estimation From Incomplete Data Via the EM Algorithm” . Journal of the Royal Statistical Society , 39 : 1 – 38 . (with discussion), Ser. B
   Google Scholar
• Dempster , A. P. , Laird , N. M. and Rubin , D. B. 1980 . “Iteratively Reweighted Least Squares for Linear Regression When Errors are Normal/Independent Distributed” . In Multivariate Analysis V , Edited by: Krishnaiah , P. R. 35 – 57 . Amsterdam : North-Holland .
   Google Scholar
• De Pierro , A. R. 1993 . “A Modified Expectation Maximization Algorithm for Penalized Likelihood Estimation in Emission Tomography” . IEEE Transactions on Medical Imaging ,
   PubMed Web of Science ®Google Scholar
• Dunnett , C. W. and Sobel , M. 1954 . “A Bivariate Generalization of Student's t Distribution With Tables for Certain Cases” . Biometrika , 41 : 153 – 169 .
   Web of Science ®Google Scholar
• Efron , B. and Hinkley , D. V. 1978 . “Assessing the Accuracy of the Maximum Likelihood Estimator: Observed Versus Fisher Information” . Biometrika , 65 : 457 – 487 . with discussion
   Web of Science ®Google Scholar
• Fang , K. T. , Kotz , S. and Ng , K. W. 1990 . Symmetric Multivariate and Related Distributions , London : Chapman and Hall .
   Google Scholar
• Feller , W. 1971 . An Introduction to Probability Theory and Its Applications, , 2nd ed. , Vol. 2 , New York : John Wiley .
   Google Scholar
• Green , P. J. 1984 . “Iteratively Reweighted Least Squares for Maximum Likelihood Estimation, and Some Robust and Resistant Alternatives” . Journal of the Royal Statistical Society , 46 : 149 – 192 . (with discussion), Ser. B
   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
• Hathaway , R. J. 1986 . “A Constrained EM Algorithm for Univariate Normal Mixtures” . Journal of Statistical Computing and Simulation , 23 : 211 – 230 .
   Web of Science ®Google Scholar
• Hogg , R. V. 1974 . “Adaptive Robust Procedures: A Partial Review and Some Suggestions for Future Applications and Theory” . Journal of the American Statistical Association , 69 : 909 – 926 . with discussion
   Web of Science ®Google Scholar
• Holland , P. W. and Welsch , R. E. 1977 . “Robust Regression Using Iteratively Reweighted Least Squares” . Communications in Statistics, Part A, Theory and Methods , 6 : 813 – 827 .
   Web of Science ®Google Scholar
• Huber , P. J. 1981 . Robust Statistics , New York : John Wiley .
   Google Scholar
• Keilson , J. and Steutel , F. W. 1974 . “Mixture of Distributions Moment Inequalities, and Measures of Exponentiality and Normality” . Annals of Probability , 2 : 112 – 130 .
   Web of Science ®Google Scholar
• Lange , K. L. , Little , R. J. A. and Taylor , J. M. G. 1989 . “Robust Modeling Using the t Distribution” . Journal of the American Statistical Association , 84 : 881 – 896 .
   Web of Science ®Google Scholar
• Mäkelainen , T. , Schmidt , K. and Styan , G. P. H. 1981 . “On the Existence and Uniqueness of the Maximum Likelihood Estimate of a Vector-Valued Parameter in Fixed-Size Samples” . The Annals of Statistics , 9 : 758 – 767 .
   Web of Science ®Google Scholar
• Malik , H. J. 1985 . “Logistic Distribution” . In Encyclopedia of Statistical Science Vol. 5: Lindeberg Conditions to Multitrait-Multimethod Matrices , Edited by: Kotz , S. and Johnson , N. L. New York : John Wiley .
   Google Scholar
• Merle , G. and Spath , H. 1974 . “Computational Experiences With Discrete Lp Approximation” . Computing , 12 : 315 – 321 .
   Web of Science ®Google Scholar
• Mosteller , F. and Tukey , J. W. 1977 . Data Analysis and Regression: A Second Course in Statistics , Reading , MA : Addison-Wesley .
   Google Scholar
• Murray , J. D. 1984 . Asymptotic Analysis , New York : Springer-Verlag .
   Google Scholar
• Press , W. H. , Flannery , B. P. , Teukolsky , S. A. and Vetterling , W. T. 1986 . Numerical Recipes: The Art of Scientific Computing , Cambridge , , U.K. : Cambridge University Press .
   Google Scholar
• Racine-Poon , A. 1989 . “A Bayesian Approach to Nonlinear Calibration Problems” . Journal of the American Statistical Association , 83 : 650 – 656 .
   Web of Science ®Google Scholar
• Rao , C. R. 1973 . Linear Statistical Inference and Its Applications, , 2nd ed. , New York : John Wiley .
   Google Scholar
• Renkin , E. M. 1959 . “Transport of Potassium-42 From Blood Tissue in Isolated Mammalian Skeletal Muscles” . American Journal of Physiology , 197 : 1205 – 1210 .
   PubMed Web of Science ®Google Scholar
• Rogers , W. H. and Tukey , J. W. 1972 . “Understanding Some Long-Tailed Distributions” . Statistica Neerlandia , 26 : 211 – 226 .
   Google Scholar
• Schelbert , H. R. , Phelps , M. E. , Huang , S. E. , MacDonald , N. S. , Hansen , H. , Selin , C. and Kuhl , D. E. 1981 . “N-13 Ammonia as an Indicator of Myocardial Blood Flow” . Circulation , 63 : 1259 – 1272 .
   PubMed Web of Science ®Google Scholar
• Schlossmacher , E. J. 1973 . “An Iterative Technique for Absolute Deviations Curve Fitting” . Journal of the American Statistical Association , 68 : 857 – 859 .
   Web of Science ®Google Scholar
• Shimizu , R. 1987 . “Error Bounds for Asymptotic Expansions of the Scale Mixtures of the Normal Distribution” . Annals of the Institute of Statistical Mathematics , 39 : 611 – 622 .
   Web of Science ®Google Scholar
• Stone , M. 1988 . “Quetelet and the Poetry of Statistical Conjecture” . Chance , 1 : 10 – 16 .
   Google Scholar
• Szatrowski , T. H. 1980 . “Necessary and Sufficient Conditions for Explicit Solutions in the Multivariate Normal Estimation Problem for Patterned Means and Covariances” . The Annals of Statistics , 8 : 802 – 810 .
   Web of Science ®Google Scholar
• Tiede , J. J. and Pagano , M. 1979 . “The Application of Robust Calibration to Radioimmunoassay” . Biometrics , 35 : 567 – 574 .
   PubMed Web of Science ®Google Scholar
• Tukey , J. W. 1960 . “A Survey of Sampling From Contaminated Distributions” . In Contributions to Probability and Statistics I , Edited by: Olkin , I. 448 – 485 . Stanford , CA : Stanford University Press .
   Google Scholar
• Wu , C. J. F. 1983 . “On the Convergence Properties of the EM Algorithm” . The Annals of Statistics , 11 : 95 – 103 .
   Web of Science ®Google Scholar