Variable Selection and Function Estimation in Additive Nonparametric Regression Using a Data-Based Prior

Journal of the American Statistical Association

Volumn 94, Issue 447, 1999, Pages 777-794

  Shively, Thomas S ^a   Kohn, Robert ^b   Wood, Sally ^b  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^b UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

Bayesian information criterion; Binary regression; Gaussian errors; Model averaging; Posterior probabilities; Time series models

Indexed keywords

EID: 0000307942     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1080/01621459.1999.10474180     Document Type: Article

References (25)

1. Albert, J., and Chib, S. (1993), "Bayesian analysis of binary and polychotomousresponsedata, " Journal of the American Statistical Association, 88, 669-679.
2. Ansley, C. E, Kohn, R., and Tharm, D. (1991), "The Performance of CrossValidation and Maximum Likelihood Estimators of Spline Smoothing Parameters, " Journal of the American Statistical Association, 86, 1042-1050.
3. Berger, J. O., and Pericchi, L. R. (1996), ''The Intrinsic Bayes Factor for Model Selection and Prediction, " Journal of the American Statistical Association, 91, 109-122.
4. Casella, G., and George, E.J. (1992), "Explaining the Gibbs Sampler, " The American Statistician, 46, 167-174.
5. Denison, D. G. T., Mallick, B. K., and Smith, A. F. M. (1998), "Automatic Bayesian Curve Fitting, " Journal of the Royal Statistical Society, Ser. B, 80, 331-350.
6. Erkanli, A., and Gopalan, R. (1996), "Bayesian Nonparametric Regression: Smoothing Using Gibbs Sampling, " in Bayesian Statistics and Econometrics: Essays in Honor of Arnold Zellner, eds. D. Berry, K. Chaloner, and J. Geweke, New York: Wiley, pp. 267-277.
7. Gelfand, A. E., and Smith, A. F. M. (1990), "Sampling-Based Approaches to Calculating Marginal Densities, " Journal of the American Statistical Association, 85, 398-409.
8. George, E. I., and McCulloch, R. E. (1993), "Variable Selection via Gibbs Sampling, " Journal of the American Statistical Association, 88, 881-889.
9. Hardie, W., and Korostelev, A. (1996), "Search for Significant Variables in Nonparametric Additive Regression, " Biometrika, 83, 541-549.
10. Harvey, A. C. (1989), Forecasting, Structural Time Series Models and the Kalman Filter, Cambridge, U.K.: Cambridge University Press.
11. Hastie, T. J., and Tibshirani, R. J. (1987), "Generalized Additive Models: Some Applications, " Journal ofthe American Statistical Association, 82, 371-386.
12. Kohn, R. (1983), "Consistent Estimation of Minimal Model Dimension, " Econometrica, 51, 367-376.
13. Min, C., and Zellner, A. (1993), "Bayesian and non-Bayesian Methods for Combining Models and Forecasts With Applications to Forecasting International Growth Rates, " Journal of Econometrics, 56, 89-118.
14. O'Hagan, A. (1995), "Fractional Bayes Factors for Model Comparison" (with discussion), Journal of the Royal Statistical Society, Ser. B, 57, 99-138.
15. Raftery, A., Madigan, D., and Hoeting, J. (1997), "Bayesian Model Averaging for Linear Regression Models, " Journal of the American Statistical Association, 92, 179-191.
16. Rao, C. R. (1973), Linear Statistical Inference and Its Applications (2nd ed.), New York: Wiley.
17. Schwartz, G. (1978), "Estimating the Dimension of a Model, " The Annals of Statistics, 6, 461-464.
18. Smith, M., and Kohn, R. (1996), "Nonparametric Regression Using Bayesian Variable Selection, " Journal of Econometrics, 75, 317-344.
19. Tierney, L. (1994), "Markov Chains for Exploring Posterior Distributions, " The Annals of Statistics, 22, 1701-1762.
20. Wahba, G. (1978), "Improper Priors, Spline Smoothing and the Problem of Guarding Against Model Errors in Regression, " Journal of the Royal Statistical Society, Ser. B, 40, 364-372.
21. Wahba, G (1990), Spline Models for Observational Data, CBMS-NSF Regional Conference Series in Applied Mathematics, Vol. 59, Philadelphia: SIAM.
22. Wahba, G., Wang, Y., Gu, C., Klein, R., and Klein, B. (1995), "Smoothing Spline ANOVA for Exponential Families, With Application to the Wisconsin Epidemiological Study of Diabetic Retinopathy, " The Annals of Statistics, 23, 1865-1895.
23. Wong, C, and Kohn, R. (1996), "A Bayesian Approach to Additive Semiparametric Regression, " Journal of Econometrics, 74, 209-235.
24. Wood, S., and Kohn, R. (1998), "A Bayesian Approach to Robust Nonparametric Binary Regression, " Journal of the American Statistical Association, 93, 203-213.
25. Wood, S., Shively, T. S., and Kohn, R. (1996), "Model Selection in Spline Nonparametric Regression, " working paper, Australian Graduate School of Management.