Robust Estimation, Nonnormalities, and Generalized Exponential Distributions

REFERENCES

• Barndorff-Nielson , O. 1978 . Information and Exponential Families in Statistical Theory New York : John Wiley. .
   Google Scholar
• Berk , R. H. 1972 . “Consistency and Asymptotic Normality of MLE's for Exponential Models” . Annals of Mathematical Statistics , 43 : 193 – 204 .
   Google Scholar
• Berndt , E. K. , Hall , B. , Hall , R. E. and Hausman , J. A. 1974 . “Estimation and Inference in Nonlinear Structural Models,” . Annals of Economic and Social Measurement , 3 : 653 – 665 .
   Google Scholar
• Bloomfield , P. and Steiger , W. L. 1983 . Least Absolute Deviations Theory: Applications and Algorithms Boston : Birkhauser. .
   Google Scholar
• Bradley , E. L. 1973 . “The Equivalence of Maximum Likelihood and Weighted Least Squares Estimates in the Exponential Family,” . Journal of the American Statistical Association , 68 : 199 – 200 .
   Web of Science ®Google Scholar
• Broyden , C. G. 1970 . “The Convergence of a Class of Double-Rank-Minimization Algorithms, 2: The New Algorithm,” . Journal of the Institute of Mathematical Applications , 6 : 222 – 231 .
   Google Scholar
• Butler , R. J. , McDonald , J. B. , Nelson , R. D. and White , S. B. 1990 . “Robust and Partially Adaptive Estimation of Regression Models,” . The Review of Economics and Statistics , 72 : 321 – 327 .
   Web of Science ®Google Scholar
• Cobb , L. 1978 . “Stochastic Catastrophe Models and Multimodal Distributions,” . Behavioural Science , 23 : 360 – 374 .
   Google Scholar
• Cobb , L. 1981 . “The Multimodal Exponential Families of Statistical Catastrophe Theory,”. ” . In Statistical Distributions in Scientific Work, 4 Edited by: Taillie , C. , Patil , G. P. and Baldessari , B. 67 – 90 . Dordrecht : Holland, Reidel Press. .
   Google Scholar
• Cobb , L. , Koppstein , P. and Chen , N. H. 1983 . “Estimation and Moment Recursion Relations for Multimodal Distributions of the Exponential Family,” . Journal of the American Statistical Association , 78 : 124 – 130 .
   Web of Science ®Google Scholar
• Cobb , L. and Zacks , S. 1985 . “Applications of Catastrophe Theory for Statistical Modeling in the Biosciences,” . Journal of the American Statistical Association , 80 : 793 – 802 .
   Web of Science ®Google Scholar
• Cox , D. R. and Hinkley , D. V. 1974 . Theoretical Statistics London : Chapman and Hall. .
   Google Scholar
• Dunning , K. A. and Hanson , J. N. 1977 . “Generalized Pearson Distributions and Nonlinear Programming,” . Communications in Statistics, Part B—Simulation and Computation , 6 : 115 – 128 .
   Google Scholar
• Fletcher , R. 1970 . “A New Approach to Variable Metrie Algorithms,” . Computer Journal , 13 : 317 – 322 .
   Web of Science ®Google Scholar
• Fletcher , R. and Powell , M. J. D. 1963 . “A Rapidly Convergent Descent Method for Minimization,” . Computer Journal , 6 : 163 – 168 .
   Web of Science ®Google Scholar
• Gabrielson , G. 1982 . “On the Unimodality of the Likelihood for the Cauchy Distribution: Some Comments,” . Biometrika , 69 : 677 – 678 .
   Web of Science ®Google Scholar
• Goldfarb , D. 1970 . “A Family of Variable Metrie Methods Derived by Variational Means,” . Mathematics of Computation , 24 : 23 – 26 .
   Web of Science ®Google Scholar
• Hogg , R. V. and Klugman , S. A. 1983 . “On the Estimation of Long-Tailed Skewed Distributions with Actuarial Applications,” . Journal of Econometrics , 23 : 91 – 102 .
   Web of Science ®Google Scholar
• Kendall , M. G. and Stuart , A. 1967 . The Advanced Theory of Statistics, , 2nd ed. Vol. 2 , London : Charles Griffen. .
   Google Scholar
• Klein , R. and Spady , R. 1984 . “Quasi-Maximum Likelihood as a Parametric Approach to Robust Estimation,” Bell Communication Research. . working paper
   Google Scholar
• Lange , K. L. , Little , J. A. and Taylor , J. M. G. 1989 . “Robust Statistical Modeling Using the t Distribution,” . Journal of the American Statistical Association , 84 : 881 – 896 .
   Web of Science ®Google Scholar
• Martin , V. L. 1990 . “Properties and Applications of Distributions from the Generalized Exponential Family,” Monash University, Mathematics Department. . unpublished Ph.D. dissertation
   Google Scholar
• Martin , V. L. 1992 . “Threshold Time Series Models as Multimodal Distribution Jump Processes,” . Journal of Time Series Analysis , 13 : 79 – 94 .
   Google Scholar
• O'Toole , A. L. 1933a . “On the System of Curves for Which the Method of Moments is the Best Method of Fitting,” . Annals of Mathematical Statistics , 4 : 1 – 29 .
   Google Scholar
• O'Toole , A. L. 1933b . “A Method of Determining the Constants in the Bimodal Fourth Degree Exponential Function,” . Annals of Mathematical Statistics , 4 : 80 – 93 .
   Google Scholar
• Rousseeuw , P. J. and van Zomeren , B. C. 1990 . “Unmasking Multivariate Outliers and Leverage Points,” . Journal of the American Statistical Association , 85 : 633 – 639 .
   Web of Science ®Google Scholar
• Shanno , D. F. 1970 . “Conditioning of Quasi-Newton Methods for Function Minimization,” . Mathematics of Computation , 24 : 647 – 656 .
   Web of Science ®Google Scholar
• Sharpe , W. F. 1964 . “Capital Asset Prices: A Theory of Equilibrium Under Conditions of Risk,” . Journal ofFinance , 19 : 425 – 442 .
   Web of Science ®Google Scholar
• Weinstein , J. A. 1976 . Demographie Transition and Social Change Morristown , N.J. : General Learning Press. .
   Google Scholar