Goodness of prediction fit for multivariate linear models

Journal of the American Statistical Association

Volumn 91, Issue 433, 1996, Pages 191-197

  Keyes, Tim K ^a   Levy, Martin S ^b  

^a GENERAL ELECTRIC COMPANY   (United States)

^b UNIVERSITY OF CINCINNATI   (United States)

Author keywords

Bayesian predictive density; Calculus of variations; Discrimination information; Kullback Leibler divergence; Predictive inference; Predictive likelihood

Indexed keywords

EID: 0042786334     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1080/01621459.1996.10476676     Document Type: Article

References (42)

1. Aitchison, J. (1975), “Goodness of Prediction Fit,” Biometrika, 62, 547-554.
2. Aitchison, J. (1990), “On Coherence in Parametric Density Estimation,” Biometrika, 77, 905-908.
3. Aitchison, J., and Dunsmore, I. (1975), Statistical Prediction Analysis, Cambridge, U.K.: Cambridge University Press.
4. Bjomstad, J. F. (1990), “Predictive Likelihood: A Review,” Statistical Science, 5, 242-265.
5. Broemeling, L. D. (1985), Bayesian Analysis of Linear Models, New York: Marcel Dekker.
6. Butler, R. W. (1986), “Predictive Likelihood Inference With Applications” (with discussion), Journal of the Royal Statistical Society, Ser. B, 48, 1-38.
7. Cox, D. R., and Hinkley, D. V. (1974), Theoretical Statistics, London: Chapman and Hall.
8. Dickey, J. M. (1966), “Matricvariate Generalizations of the Multivariate t Distribution and the Inverted Multivariate t Distribution,” The Annals of Mathematical Statistics, 38, 511-518.
9. El-Sayyad, G. M., Samiuddin, M., and Al-Harbey, A. A. (1989), “On Parametric Density Estimation,” Biometrika, 76, 343-348.
10. Faulkenberry, G. D., and Lejeune, M. (1982), “A Simple Predictive Density Function,” Journal of the American Statistical Association, 77,654-657.
11. Geisser, S. (1965), “Bayesian Estimation in Multivariate Analysis,” Annals of Mathematical Statistics, 36, 150-159.
12. Geisser, S. (1971), “The Inferential Use of Predictive Distributions,” in Foundations of Statistical Inference, eds. V. P. Godambe and D. A. Sprott, Toronto: Holt, Rinehart, and Winston, pp. 459-469.
13. Geisser, S. (1993), Predictive Inference: An Introduction, New York: Chapman and Hall.
14. Geisser, S., and Cornfield, I. (1963), “Posterior Distributions for Multivariate Normal Classifications,” Journal of the Royal Statistical Society, Ser. B, 25, 368-376.
15. Gelfand, I., and Fomin, S. (1963), Calculus of Variations, Selected Russian Publications in the Mathematical Sciences, Englewood Cliffs, NJ: Prentice-Hall.
16. Ghurye, S. G., and Olkin, I. (1969), “Unbiased Estimation of Some Multivariate Probability Densities and Related Functions,” The Annals of Mathematical Statistics, 40, 1261-1271.
17. Guttman, I., and Hougaard, P. (1985), “Studentization and Prediction Problems in Multivariate Multiple Regression,” Communications in Statistics, Part A-Theory and Methods, 14, 1251-1258.
18. Harris, I. R. (1989), “Predictive Fit for Natural Exponential Families,” Biometrika, 76, 675-684.
19. Hinkley, D. V. (1979), “Predictive Likelihood,” The Annals of Statistics, 1, 718-728.
20. Kalbfleish, S., and Sprott, D. A. (1969), “Applications of Likelihood and Fiducial Probability to Sampling Finite Populations,” in New Developments in Survey Sampling, eds. N. Johnson and H. Smith, New York: Wiley-Interscience, pp. 359-389.
21. Keyes, T. K., and Levy, M. S. (1993), “On Consistency of Some Predicting Densities for the Multivariate Linear Model,” Unpublished technical re-port, University of Cincinnati, Dept, of Quantitative Analysis, to appear in Mathematical Methods of Statistics.
22. Keyes, T. K., and Levy, M. S. (1996), “Optimal Control Designs Using Predicting Densities for the Multivariate Linear Model,” Communications in Statistics: Theory and Methods, 25.
23. Kullback, S., and Leibler, R. A. (1951), “On Information and Sufficiency,” The Annals of Mathematical Statistics, 22, 79-86.
24. Lauritzen, S. L. (1974), “Sufficiency, Prediction and Extreme Models,” Scandinavian Journal of Statistics, 1, 128-134.
25. Levy, M. S. (1987), “A Numerical Comparison of Some Prediction Densities for the Normal Linear Model,” Computational Statistics & Data Analysis, 5, 45-51.
26. Levy, M. S., and Pemg, S. K. (1984), “A Maximum Likelihood Prediction Function for the Linear Model With Consistency Results,” Communica-tions in Statistics, Part A-Theory and Methods, 13, 1257-1273.
27. Levy, M. S., and Pemg, S. K. (1986), “An Optimal Prediction Function for the Normal Linear Model,” Journal of the American Statistical Association, 81, 196-198.
28. Murray, G. D. (1997), “A Note on the Estimation of Probability Density Functions,” Biometrika, 64, 150-152.
29. Murray, G. D. (1979), 'The Estimation of Multivariate Density Functions Using Incomplete Data,” Biometrika, 66, 375-380.
30. Nel, D. G., de Waal, D. J., and Marx, D. G. (1984), “A Predictive Approach to the Detection of Additional Information in a Multivariate Regression Model,” Communications in Statistics, Part A-Theory and Methods, 13, 2119-2132.
31. Ng, V. M. (1980), “On the Estimation of Parametric Density Functions,” Biometrika, 67, 505-506.
32. O'Reilly, F. J. (1975), “On a Criterion for Extrapolation in Normal Regression,” The Annals of Statistics, 3, 219-222.
33. O'Reilly, F. J. (1976), “On a Criterion for Simultaneous Extrapolation in Nonfull Rank Normal Regression,” The Annals of Statistics, 4, 625-628.
34. O'Reilly, F. J., and Diaz, J. (1980), “Correction to: On a Criterion for Simultaneous Extrapolation in Nonfull Rank Normal Regression,” The Annals of Statistics, 8, 1177-1178.
35. O'Reilly, F. J., and Zarate, G. P. (1984), “On the MVUE for the Distribution of the Multivariate Normal Regression,” Journal of Statistical Planning and Inference, 10, 273-276.
36. Press, S. J. (1972), Applied Multivariate Analysis, New York: Holt, Rinehart and Winston.
37. Raiffa, H., and Schlaifer, R. (1961), Applied Statistical Decision Theory, Harvard University, Division of Research, Graduate School of Business Administration.
38. Soofi, E. S. (1994), “Capturing the Intangible Concept of Information,” Journal of the American Statistical Association, 89, 1243-1254.
39. Wilkinson, G. N. (1977), “On Resolving the Controversy in Statistical Inference,” Journal of the Royal Statistical Society, Ser. B, 39, 119-171.
40. Zellner, A. (1991), “Bayesian Methods and Entropy in Economics and Econometrics,” in Maximum Entropy and Bayesian Methods, eds. W. T. Grandy Jr., and L. H. Schick, Dordrecht: Kluwer.
41. Zellner, A. (1993), “Model, Prior Information and Bayesian Analysis,” working paper, University of Chicago, Graduate School of Business.
42. Zellner, A., and Chetty, V. K. (1965), “Prediction and Decision Problems in Regression Models from the Bayesian Point of View,” Journal of the American Statistical Association, 60, 608-616.