Regression trees with unbiased variable selection and interaction detection

Statistica Sinica

Volumn 12, Issue 2, 2002, Pages 361-386

  Loh, Wei Yin ^a  

^a University of Wisconsin Madison   (United States)

Author keywords

Bagging; Bias correction; Bootstrap; Interaction detection; Piecewise linear

Indexed keywords

EID: 0036556537     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (28)

1. Ahn, H. and Loh, W.-Y. (1994). Tree-structured proportional hazards regression modeling. Biometrics 50, 471-485.
2. Alexander, W. P. and Grimshaw, S. D. (1996). Treed regression. J. Comput. Graph. Statist. 5, 156-175.
3. Belsley, D. A. and Kuh, E. and Welsch, R. E. (1980). Regression Diagnostics: Identifying Influential Data and Sources of Collinearity. Wiley, New York.
4. Borggaard, C. and Thodberg, H. H. (1992). Optimal minimal neural interpretation of spectra. Anal. Chemistry 64, 545-551.
5. Breiman, L. (1996). Bagging predictors. Machine Learning 24, 123-140.
6. Breiman, L., Friedman, J. H., Olshen, R. A. and Stone, C. J. (1984). Classification and Regression Trees. Wadsworth, Belmont.
7. Chaudhuri, P. and Loh, W.-Y. (1998). Quantile regression trees. Technical Report 994, Department of Statistics, University of Wisconsin, Madison.
8. Chaudhuri, P., Huang, M.-C., Loh, W.-Y. and Yao, R. (1994). Piecewise-polynomial regression trees. Statist. Sinica 4, 143-167.
9. Chaudhuri, P., Lo, W.-D., Loh, W.-Y. and Yang, C.-C. (1995). Generalized regression trees. Statist. Sinica 5, 641-666.
10. Chipman, H., George, E. I. and McCulloch, R. E. (1998). Bayesian CART Model Search (with discussion). J. Amer. Statist. Assoc. 93, 935-960.
11. Ciampi, A., Hogg, S. A., McKinney, S. and Thiffault, J. (1988). RECPAM: A computer program for recursive partition and amalgamation for censored survival data and other situations frequently occurring in biostatistics, I: Methods and program features. Comput. Methods and Programs in Biomedicine 26, 239-256.
12. Ciampi, A., Lou, Z., Lin, Q. and Negassa, A. (1991). Recursive partition and amalgamation with the exponential family: theory and applications. Appl. Stochastic Models Data Anal. 7, 121-137.
13. Conlon, M. and Meyer, J. (1988). Baseball performance and salaries. ASA 1988 Proceedings of the Section on Statistical Graphics, 98-103. American Statistical Association, Alexandria, VA.
14. Denison, D. G., Mallick, B. K. and Smith, A. F. M. (1998). A Bayesian CART algorithm. Biometrika 85, 363-377.
15. Doyle, P. (1973). The use of automatic interaction detector and similar search procedures. Oper. Res. Quarterly 24, 465-467.
16. Fielding, A. (1977). Binary segmentation: the automatic detector and related techniques for exploring data structure. In The Analysis of Survey Data, Volume I, Exploring Data Structures (Edited by C. A. O'Muircheartaigh and C. Payne). Wiley, New York.
17. Friedman, J. H. (1991). Multivariate adaptive regression splines (with discussion). Ann. Statist. 19, 1-141.
18. Hawkins, D. M. (1997). FIRM: Formal inference-based recursive modeling. PC version, Release 2.1. Technical Resport 546, School of Statistics, University of Minnesota.
19. Hoaglin, D. C. and Velleman, P. F. (1995). A critical look at some analyses of major league baseball salaries. Amer. Statist. 49, 277-285.
20. Kass, G. V. (1975). Significance Testing in Automatic Interaction Detection (A.I.D.). Appl. Statist. 24, 178-189.
21. Kim, H. and Loh, W.-Y. (2001). Classification trees with unbiased multiway splits. J. Amer. Statist. Assoc. 96, 589-604.
22. Levene, H. (1960). Robust tests for equality of variances. In Contributions to Probability and Statistics (Edited by I. Olkin, S. G. Ghurye, W. Hoeffding, W. G. Madow and H. B. Mann), 278-292. Stanford University Press, Palo Alto.
23. Li, K.-C., Lue, H.-H. and Chen, C.-H. (2000). Interactive tree-structured regression via principal Hessian directions. J. Amer. Statist. Assoc. 95, 547-560.
24. Loh, W.-Y. and Vanichsetakul, N. (1988). Tree-structured classification via generalized discriminant analysis (with discussion). J. Amer. Statist. Assoc. 83, 715-728.
25. Marshall, R. J. (1995). A program to implement a search method for identification of clinical subgroups. Statist. in Medicine 14, 2645-2659.
26. Merz, C. J. and Murphy, P. M. (1996). UCI repository of machine learning databases. Department of Information and Computer Science, University of California, Irvine, CA. (http://www.ics.uci.edu/̃relearn/MLRepository.html).
27. Morgan, J. N. and Sonquist, J. A. (1963). Problems in the analysis of survey data, and a proposal. J. Amer. Statist. Assoc. 58, 415-434.
28. Thodberg, H. H. (1996). A Review of Bayesian neural networks with an application to near infrared spectroscopy. IEEE Transactions on Neural Networks 7, 56-72.