A Maximum Entropy Approach to Recovering Information from Multinomial Response Data

References

• Agmon , N. , Alhassid , Y. and Levine , R. D. 1979 . “An Algorithm for Finding the Distribution of Maximal Entropy,” . Journal of Computational Physics , 30 : 250 – 259 .
   Web of Science ®Google Scholar
• Albert , J. H. and Chib , S. 1993 . “Bayesian Analysis of Binary and Poly-chotomous Response Data,” . Journal of the American Statistical Association , 88 : 669 – 679 .
   Web of Science ®Google Scholar
• Amemiya , T. 1985 . Advanced Econometrics , Cambridge , MA : Harvard University Press .
   Google Scholar
• Behara , M. 1990 . Additive and Nonadditive Measures of Entropy , New York : John Wiley .
   Google Scholar
• Belsley , D. A. 1991 . Conditioning Diagnostics , New York : John Wiley .
   Google Scholar
• Csiszár , I. 1991 . “Why Least Squares and Maximum Entropy? An Axiomatic Approach to Inference for Linear Inverse Problems,” . The Annals of Statistics , 19 : 2032 – 2066 .
   Web of Science ®Google Scholar
• Denzau , A. T. , Gibbons , P. C. and Greenberg , E. 1989 . “Bayesian Estimation of Proportions With a Cross-Entropy Prior,” . Communications in Statistics, Part A—Theory And Methods , 18 : 1843 – 1861 .
   Web of Science ®Google Scholar
• Donoho , D. L. , Johnstone , I. M. , Hoch , J. C. and Stern , A. S. 1992 . “Maximum Entropy and the Nearly Black Object,” . Journal of the Royal Statistical Society , 54 : 41 – 81 . Ser. B
   Google Scholar
• Gokhale , D. V. and Kullback , S. 1978 . The Information in Contingency Tables , New York : Marcel Dekker .
   Google Scholar
• Golan , A. 1988 . “A Discrete Stochastic Model of Economic Production and a Model of Fluctuations in Production—Theory and Empirical Evidence,” , University of California, Berkeley . unpublished doctoral thesis
   Google Scholar
• Golan , A. 1994 . “A Multivariable Stochastic Theory of Size Distribution of Firms With Empirical Evidence,” . Advances in Econometrics , 10 : 1 – 46 .
   Google Scholar
• Golan , A. , Judge , G. and Perloff , J. 1995 . “Estimation and Inference With Censored and Ordered Multinomial Response Data,” , University of California, Berkeley . unpublished paper
   Google Scholar
• Good , I. J. 1963 . “Maximum Entropy for Hypothesis Formulation, Especially for Multidimensional Contingency Tables,” . Annals of Mathematical Statistics , 34 : 911 – 934 .
   Google Scholar
• Greene , W. H. 1993 . Econometric Analysis, , 2nd ed. , New York : Macmillan .
   Google Scholar
• Griffiths , W. E. , Hill , R. C. and Pope , P. J. 1987 . “Small-Sample Properties of Probit Model Estimators,” . Journal of the American Statistical Association , 82 : 929 – 937 .
   Web of Science ®Google Scholar
• Hastie , T. , Buja , A. and Tibshirani , R. 1993 . “Penalized Discriminant Analysis,” , Bell Laboratories . unpublished paper
   Google Scholar
• Jaynes , E. T. 1957a . “Information Theory and Statistical Mechanics,” . Physics Review , 106 : 620 – 630 .
   Google Scholar
• Jaynes , E. T. 1957b . “Information Theory and Statistical Mechanics II,” . Physics Review , 108 : 171 – 190 .
   Google Scholar
• Jaynes , E. T. 1984 . “Prior Information and Ambiguity in Inverse Problems,” . In Inverse Problems , Edited by: McLaughlin , D. W. 151 – 166 . Providence RI : American Mathematical Society .
   Google Scholar
• Judge , G. G. 1991 . “A Reformulation of III-Posed Inverse Problems With Noise,” , Berkeley : University of California . unpublished manuscript
   Google Scholar
• Judge , G. G. , Golan , A. and Miller , D. 1993 . “Recovering Information in the Case of III-Posed Inverse Problems With Noise,” , Berkeley : University of California . unpublished manuscript
   Google Scholar
• Judge , G. G. , Griffiths , W. E. , Hill , R. C. , Lütkepohl , H. and Lee , T.-C. 1985 . The Theory and Practice of Econometrics, , 2nd ed. , New York : John Wiley .
   Google Scholar
• Koop , G. and Poirier , D. J. 1993 . “Bayesian Analysis of Logit Models Using Natural Conjugate Priors,” . Journal of Econometrics , 56 : 323 – 340 .
   Web of Science ®Google Scholar
• Kullback , J. 1959 . Information Theory and Statistics , New York : John Wiley .
   Google Scholar
• Le Cessie , S. and van Houwelingen , J. C. 1992 . “Ridge Estimators in Logistic Regression,” . Journal of Applied Statistics , 41 : 191 – 201 .
   Web of Science ®Google Scholar
• Lehmann , E. 1983 . Theory of Point Estimation , New York : John Wiley .
   Google Scholar
• Levine , R. D. 1980 . “An Information Theoretical Approach to Inversion Problems,” . Journal of Physics , 13 : 91 – 108 . Ser. A
   Google Scholar
• Long , J. S. 1983 . “A Graphical Method for the Interpretation of Multinomial Logit Analysis,” . Sociological Methods and Research , 15 : 420 – 446 .
   Web of Science ®Google Scholar
• Maddala , G. S. 1983 . Limited Dependent and Qualitative Variables in Econometrics , Cambridge , , UK : Cambridge University Press .
   Google Scholar
• Mallows , C. L. 1973 . “Some Comments on Cp,” . Technometrics , 15 : 661 – 665 .
   Web of Science ®Google Scholar
• Manski , C. and McFadden , D. , eds. 1981 . Structural Analysis of Discrete Data with Econometric Applications , Cambridge , MA : MIT Press .
   Google Scholar
• McFadden , D. 1974 . “Conditional Logit Analysis of Qualitative Choice Behavior,” . In Frontiers of Econometrics , Edited by: Zarembka , P. 105 – 142 . New York : Academic Press .
   Google Scholar
• Miller , D. J. 1994 . “Entropy and Information Recovery in Linear Economic Models,” , Berkeley : University of California . unpublished doctoral thesis
   Google Scholar
• O'Sullivan , F. 1986 . “A Statistical Perspective on Ill-Posed Inverse Problems,” . Statistical Science , 1 : 502 – 527 .
   Google Scholar
• Shannon , C. E. 1948 . “A Mathematical Theory of Communication,” . Bell System Technical Journal , 27 : 379 – 423 .
   Web of Science ®Google Scholar
• Soofi , E. S. 1992 . “A Generalizable Formulation of Conditional Logit With Diagnostics,” . Journal of the American Statistical Association , 87 : 812 – 816 .
   Web of Science ®Google Scholar
• Soofi , E. S. 1994 . “Capturing the Intangible Concept of Information,” . Journal of the American Statistical Association , 89 : 1243 – 1254 .
   Web of Science ®Google Scholar
• Tikhonov , A. N. and Arsenin , V. Y. 1977 . Solutions of III-Posed Problems , Washington , DC : Winston .
   Google Scholar
• Zellner , A. 1993 . “Bayesian and Non-Bayesian Estimation Using Balanced Loss Functions,” . In Statistical Decision Theory: Theory and Related Topics , Edited by: Gupta , S. S. and Berger , J. O. 377 – 390 . New York : Springer-Verlag .
   Google Scholar
• Zellner , A. and Rossi , P. E. 1984 . “Bayesian Analysis of Dichotomous Quantal Response Models,” . Journal of Econometrics , 25 : 365 – 393 .
   Web of Science ®Google Scholar