Adaptive model selection and assessment for exponential family distributions

Technometrics

Volumn 46, Issue 3, 2004, Pages 306-317

  Shen, Xiaotong ^a   Huang, Hsin Cheng ^b   Ye, Jimmy ^c  

^a UNIVERSITY OF MINNESOTA   (United States)

^b INSTITUTE OF STATISTICAL SCIENCE   (Taiwan)

^c CITY UNIVERSITY OF NEW YORK   (United States)

Author keywords

Adaptive penalty; Cross validation; Loss estimation; Parametric and nonparametric regression; Trees; Variable selection

Indexed keywords

ADAPTIVE PENALTY; CROSS-VALIDATION; LOSS ESTIMATION; PARAMETRIC AND NONPARAMETRIC REGRESSION; VARIABLE SELECTION;

COMPUTER SIMULATION; DATA MINING; MATHEMATICAL MODELS; PARAMETER ESTIMATION; POISSON DISTRIBUTION; PROBLEM SOLVING; REGRESSION ANALYSIS; TREES (MATHEMATICS);

ADAPTIVE CONTROL SYSTEMS;

EID: 4544352662     PISSN: 00401706     EISSN: None     Source Type: Trade Journal    
DOI: 10.1198/004017004000000338     Document Type: Article

References (23)

1. Akaike, H. (1973), "Information Theory and the Maximum Likelihood Principle," in International Symposium on Information Theory, eds. V. Petrov and F. Csáki, Budapest: Akademiai Kiádo, pp. 267-281.
2. Breiman, L., Friedman, J. H., Olshen, R. A., and Stone, C. J. (1984), Classification and Regression Trees, Belmont, CA: Wadsworth.
3. Burnham, K. P., and Anderson, D. R. (2002), "Model Selection and Inference," A Practical Information-Theoretic Approach (2nd ed.), New York: Spinger-Verlag.
4. Efron, B. (1983), "Estimating the Error Rate of a Prediction Rule: Improvement on Cross-Validation," Journal of the American Statistical Association, 78, 316-331.
5. _ (1986), "How Biased Is the Apparent Error Rate of a Prediction Rule?" Journal of the American Statistical Association, 81, 461-470.
6. Friedman, J. (1991), "Multivariate Adaptive Regression Splines" (with discussion), The Annals of Statistics, 19, 1-141.
7. George, E. I., and Foster, D. P. (2000), "Calibration and Empirical Bayes Variable Selection," Biometrika, 87, 731-747.
8. Hagen, J. A., Nafstad, P., Skrondal, A., Bjorkly, J., and Magnus, P. (2000), "Associations Between Outdoor Air Pollutants and Hospitalization for Respiratory Diseases," Epidemiology, 11, 136-140.
9. Lin, X., Wahba, G., Xiang, D., Gao, F., Klein, R., and Klein, B. (2000), "Smoothing Spline ANOVA Models for Large Data Sets With Bernoulli Observations and the Randomized GACV," The Annals of Statistics, 28. 1570-1600.
10. Linhart, H., and Zucchini, W. (1986), Model Selection, New York: Wiley.
11. Linn, W. S., Szlachcic, Y., Gong, H., Jr., Kinney, P. L., and Berhane, K. T. (2000), "Air Pollution and Daily Hospital Admissions in Metropolitan Los Angeles," Environmental Health Perspectives, 108, 427-434.
12. Luo, Z., and Wahha, G. (1997), "Hybrid Adaptive Splines,'' Journal of the American Statistical Association, 92, 107-116.
13. McCullagh. P., and Nelder, J. A. (1989), Generalized Linear Models (2nd ed), London: Chapman & Hall.
14. Moolgavkar, S. H., Luebeck, E. G., and Anderson, E. L. (1997), "Air Pollution and Hospital Admissions for Respiratory Causes in Minneapolis-St. Paul and Birmingham," Epidemiology, 8, 364-370.
15. Nagelkerke, N. J. D. (1991), "A Note on a General Definition of the Coefficient of Determination," Biometrika, 78, 691-692.
16. Schwarz, G. (1978), "Estimating the Dimension of a Model," The Annals of Statistics, 6, 461-464.
17. Sheppard, L., Levy. D., Morris. G., Larson, T. V., and Koenig, J. Q. (1999), "Effects of Ambient Air Pollution on Nonelderly Asthma Hospital Admission in Seattle. Washington, 1987-1994," Epidemiology, 10, 23-30.
18. Shen, X., and Ye, J. (2002), "Adaptive Model Selection," Journal of the American Statistical Association, 97, 210-221.
19. Stein (1981), "On Multivariate Normal Mean Problems," The Annals of Siatistics, 9, 1135-1151.
20. Xiang, D., and Wahba, G. (1996), "A Generalized Approximate Cross-Validation for Smoothing Splines With Non-Gaussian Data," Statistica Sinica, 6, 675-692.
21. Ye, J. (1998), "On Measuring and Correcting the Effects of Data Mining and Model Selection," Journal of the American Statistical Association, 93, 120-131.
22. Ye, J., and Wong, W. H. (1996), "Inference for Highly Irregular Statistics," manuscript.
23. Wong, W. H. (1992), "Estimation of the Loss of an Estimate," Technical Report 356, University of Chicago, Dept. of Statistics.