On the recovery of joint distributions from limited information

Journal of Econometrics

Volumn 107, Issue 1-2, 2002, Pages 259-274

  Miller, Douglas J ^a   Liu, Wei Han ^a  

^a PURDUE UNIVERSITY   (United States)

Author keywords

Copula; Fixed marginal distributions; Fr chet bounds; Kullback Leibler cross entropy; Maximum entropy; Minimum cross entropy; Shannon entropy

Indexed keywords

ENTROPY; INFORMATION THEORY; PARAMETER ESTIMATION; PROBABILITY DENSITY FUNCTION; RANDOM PROCESSES;

CROSS ENTROPY (CE); LIKELIHOOD CROSS VALIDATION (LCV); SHANNON ENTROPY;

INDUSTRIAL ECONOMICS;

EID: 0012495069     PISSN: 03044076     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4076(01)00123-3     Document Type: Article

References (63)

1. Arizono I., Ohta H. A test for normality based on Kullback-Leibler information. The American Statistician. 43:1989;20-22.
2. Barron A., Sheu C.-H. Approximation of density functions by sequences of exponential families. Annals of Statistics. 19:1991;1347-1369.
3. Berger J.O. Statistical Decision Theory and Bayesian Analysis. 1985;Springer, Berlin.
4. Bickel P., Ritov Y., Wellner J. Efficient estimation of linear functionals of a probability measure. p with known marginal distributions Annals of Statistics. 19:1991;1316-1346.
5. Chakak A., Koehler K. A strategy for constructing multivariate distributions. Communications in Statistics: Simulation. 24:1995;537-550.
6. Cobb L., Koppstein P., Chen N.H. Estimation and moment recursion relations for multimodal distributions of the exponential family. Journal of the American Statistical Association. 78(381):1983;124-130.
7. Cover T., Thomas J. Elements of Information Theory. 1991;Wiley, New York.
8. Crain B. An information theoretic approach to approximating a probability distribution. SIAM Journal of Applied Mathematics. 32:1977;339-346.
9. Csiszár I. I-divergence geometry of probability distributions and minimization problems. Annals of Probability. 3:1975;146-158.
10. Dall'Aglio G. Fréchet classes: the beginnings. Dall'Aglio G., Kotz S., Salineti G. Advances in Probability Distributions with Given Marginals. 1991;Kluwer Academic Publishers, Dordrecht.
11. Deming W.E., Stephan F. On a least squares adjustment of a sampled frequency table when the expected marginal totals are known. Annals of Mathematical Statistics. 11:1940;423-444.
12. Devroye L. A Course in Density Estimation. 1987;Birkhäuser, Boston.
13. Ebrahimi N., Habibullah M., Soofi E. Testing exponentiality based on Kullback-Leibler information. Journal of the Royal Statistical Society, Series B. 54:1992;739-748.
14. Emrich L., Piedmonte M. A method for generating high-dimensional binary variates. The American Statistician. 45:1991;302-304.
15. Fackler P. Modeling interdependence: an approach to simulation and elicitation. American Journal of Agricultural Economics. 73:1991;1091-1097.
16. Fréchet M. Sur les tableaux de corrélation dont les marges son données. Annales of the University of Lyon, Section A. 14:1951;53-77.
17. Frees E., Carriere J., Valdez E. Annuity valuation with dependent mortality. Journal of Risk and Insurance. 63:1996;229-261.
18. Genest C., MacKay J. The joy of copulas: bivariate distributions with uniform marginals. The American Statistician. 40(4):1986;280-283.
19. Gokhale D.V., Kullback S. The Information in Contingency Tables. 1978;Marcel Dekker, New York.
20. Golan A., Judge G., Miller D. Maximum Entropy Econometrics: Robust Estimation with Limited Data. 1996;Wiley, Chichester, UK.
21. Good I.J. Maximum entropy for hypothesis formation, especially for multidimensional contingency tables. Annals of Mathematical Statistics. 34:1963;911-934.
22. Guerrero J.-L. Multivariate mutual information: sampling distribution with applications. Communications in Statistics: Theory and Methods. 23:1994;1319-1339.
23. Haberman S. Adjustment by minimum discriminant information. Annals of Statistics. 12:1984;971-988.
24. Hall P. On Kullback-Leibler loss and density estimation. Annals of Statistics. 15:1987;1491-1519.
25. Hoeffding W. Masstabinvariente korrelationstheorie. Schriften des mathematischen Instituts und des Instituts für Angewandt Mathematik der Universitat Berlin. 5:1940;179-233.
26. Hong, Y., White, H., 2000. Asymptotic distribution theory for nonparametric entropy measures of serial dependence. Working paper. University of California, San Diego.
27. Huang J., Kotz S. Correlation structure in iterated Farlie-Gumbel-Morgenstern distributions. Biometrika. 71:1984;633-636.
28. Ireland C., Kullback S. Contingency tables with given marginals. Biometrika. 55:1968;179-188.
29. Jansen M. Maximum entropy distributions with prescribed marginals and normal score correlation. Benes V., Stepán J. Distributions with Given Marginals and Moment Problems. 1997;Kluwer Academic Publishers, Dordrecht.
30. Jaynes, E.T., 1957a. Information theory and statistical mechanics, I Physics Review 106 620-630.
31. Jaynes, E.T., 1957b. Information theory and statistical mechanics, II Physics Review 108 171-190.
32. Joe H. Relative entropy measures of multivariate dependence. Journal of the American Statistical Association. 84:1989;157-164.
33. Joe H. Parametric families of multivariate distributions with given marginals. Journal of Multivariate Analysis. 46:1993;262-282.
34. Joe H. Multivariate Models and Dependence Concepts. 1997;Chapman & Hall, London.
35. Johnson M.E., Tenenbein A. A bivariate distribution family with specified marginals. Journal of the American Statistical Association. 76(373):1981;198-201.
36. Johnson N., Kotz S. On some generalized Farlie-Gumbel-Morgenstern distributions. Communications in Statistics. 4:1975;415-427.
37. Johnson N., Kotz S. On some generalized Farlie-Gumbel-Morgenstern distributions II: regression, correlation, and further generalizations. Communications in Statistics. 6:1977;485-496.
38. Klaassen C., Wellner J. Efficient estimation in the bivariate normal copula model: normal margins are least favourable. Bernoulli. 3:1997;55-77.
39. Klugman S., Parsa R. Fitting bivariate loss distributions with copulas. Insurance: Mathematics and Economics. 24:1999;139-148.
40. Kotz S., Seeger J.P. A new approach to dependence in multivariate distributions. Dall'Aglio G., Kotz S., Salineti G. Advances in Probability Distributions with Given Marginals. 1991;Kluwer Academic Publishers, Dordrecht.
41. Kullback S. Probability densities with given marginals. Annals of Mathematical Statistics. 39:1968;1236-1243.
42. Lee A. Generating random binary deviates having fixed marginal distributions and specified degrees of association. The American Statistician. 47:1993;209-215.
43. Long D., Krzysztofowicz R. A family of bivariate densities constructed from marginals. Journal of the American Statistical Association. 90(430):1995;739-746.
44. Maasoumi E. A compendium to information theory in economics and econometrics. Econometric Reviews. 12:1993;137-181.
45. Maasoumi, E., Racine, J., 2002. Entropy and the predictability of stock market returns. Annals Journal of Econometrics, to appear.
46. Marshall A., Olkin I. Families of multivariate distributions. Journal of the American Statistical Association. 83:1988;834-841.
47. Marton K. Bounding. d̄ -distance by informational divergence: a method to prove measure concentration Annals of Probability. 24:1996;857-866.
48. Mead L.R., Papanicolaou N. Maximum entropy in the problem of moments. Journal of Mathematical Physics. 25(8):1984;2404-2417.
49. Miller, D., 1995. On deriving joint densities of correlated prices and yields. Working paper, Iowa State University.
50. Miller, D., Liu, W.-H., 2001. Optimal hedging in an emerging market: a copula model of heavy-tailed log returns. Working paper, Purdue University.
51. Mittelhammer R., Judge G., Miller D. Econometric Foundations. 2000;Cambridge University Press, Cambridge.
52. Mittelhammer R.C. Mathematical Statistics for Economics and Business. 1996;Springer, New York.
53. Nelsen R.B. An Introduction to Copulas. 1999;Springer, New York.
54. Ormeneit D., White H. An efficient algorithm to compute maximum entropy densities. Econometric Reviews. 18:1999;127-140.
55. Pinsker M.S. Information and information stability of random variables and processes. 1964;Holden Day, San Francisco.
56. Reiss R., Thomas M. Statistical Analysis of Extreme Values. 2001;Birkhäuser, Basel, Switzerland.
57. Richardson J., Klose S., Gray A. An applied procedure for estimating and simulating multivariate empirical (MVE) probability distributions in farm-level risk assessment and policy analysis. Journal of Agricultural and Applied Economics. 32:2000;299-315.
58. Ryu H.K. Maximum entropy estimation of density and regression functions. Journal of Econometrics. 56:1993;397-440.
59. Schucany W., Parr W., Boyer J. Correlation structure in Farlie-Gumbel-Morgenstern distributions. Biometrika. 65:1978;650-653.
60. Sklar A. Fonctions de répartition a. n dimensions et leurs marges Publications de l'Institut de Statistique de l'Université de Paris. 8:1959;229-231.
61. Taylor C.R. Two practical procedures for estimating multivariate nonnormal probability density functions. American Journal of Agricultural Economics. 72:1990;210-217.
62. Tiit E.-M., Käärik E. Generation and investigation of multivariate distributions having fixed discrete marginals. Prat A. COMPSTAT: proceedings in computational statistics. 1996;Physica-Verlag, Wurzberg.
63. Zellner A., Highfield R.A. Calculation of maximum entropy distributions and approximation of marginal posterior distributions. Journal of Econometrics. 37:1988;195-209.