Focused information criterion and model averaging for generalized additive partial linear models

Annals of Statistics

Volumn 39, Issue 1, 2011, Pages 174-200

  Zhang, Xinyu ^a   Liang, Hua ^b  

^a INSTITUTE OF SYSTEMS SCIENCE   (China)

^b UNIVERSITY OF ROCHESTER   (United States)

Author keywords

Additive models; Backfitting; Focus parameter; Generalized partially linear models; Marginal integration; Model average; Model selection; Polynomial spline; Shrinkage methods

Indexed keywords

EID: 79551608669     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/10-AOS832     Document Type: Article

References (47)

1. AKAIKE, H. (1973). Maximum likelihood identification of Gaussian autoregressive moving average models. Biometrika 22 203-217. MR0326953
2. BATES, J. M. andGRANGER, C. M. J. (1969). The combination of forecasts. Operations Res. Quart. 20 451-468. MR0295497
3. BUCKLAND, S. T., BURNHAM, K. P. and AUGUSTIN, N. H. (1997). Model selection: An integral part of inference. Biometrics 53 603-618.
4. BUJA, A., HASTIE, T. and TIBSHIRANI, R. (1989). Linear smoothers and additive models (with discussion). Ann. Statist. 17 453-555. MR0994249
5. BURNHAM, K. P. and ANDERSON, D. R. (2002). Model Selection and Multimodel Inference: A Practical Information Theoretic Approach, 2nd ed. Springer, New York. MR1919620
6. CARROLL, R. J., FAN, J., GIJBELS, I. andWAND, M. P. (1997). Generalized partially linear singleindex models. J. Amer. Statist. Assoc. 92 477-489. MR1467842
7. CLAESKENS, G. and CARROLL, R. J. (2007). An asymptotic theory for model selection inference in general semiparametric problems. Biometrika 94 249-265. MR2331485
8. CLAESKENS, G., CROUX, C. and VAN KERCKHOVEN, J. (2006). Variable selection for logistic regression using a prediction-focused information criterion. Biometrics 62 972-979. MR2297667
9. CLAESKENS, G., CROUX, C. and VAN KERCKHOVEN, J. (2007). Prediction-focused model selection for autoregressive models. Aus. J. Statist. 49 359-379. MR2413576
10. CLAESKENS, G. and HJORT, N. L. (2003). The focused information criterion (with discussion). J. Amer. Statist. Assoc. 98 900-916. MR2041482
11. CLAESKENS, G. andHJORT, N. L. (2008). Model Selection and Model Averaging. Cambridge Univ. Press, Cambridge. MR2431297
12. DANILOV, D. andMAGNUS, J. R. (2004). On the harm that ignoring pretesting can cause. J. Econometrics 122 27-46. MR2082531
13. DE BOOR, C. (2001). A Practical Guide to Splines. Springer, New York. MR1900298
14. DRAPER, D. (1995). Assessment and propagation of model uncertainty. J. R. Stat. Soc. Ser. B 57 45-70. MR1325378
15. FAN, J., FENG, Y. and SONG, R. (2009). Nonparametric independence screening in sparse ultrahigh dimensional additive models. Technical report, Dept. Operations Research and Financial Engineering, Princeton Univ.
16. HAND, D. J. and VINCIOTTI, V. (2003). Local versus global models for classification problems: Fitting models where it matters. Amer. Statist. 57 124-131. MR1977118
17. HANSEN, B. E. (2005). Challenges for econometric model selection. Econ. Theory 21 60-68. MR2161958
18. HASTIE, T. J. and TIBSHIRANI, R. J. (1990). Generalized Additive Models. Chapman & Hall, London. MR1082147
19. HÄRDLE, W., HUET, S., MAMMEN, E. and SPERLICH, S. (2004a). Bootstrap inference in semiparametric generalized additive models. Econom. Theory 20 265-300. MR2044272
20. HÄRDLE, W., MÜLLER, M., SPERLICH, S. andWERWATZ, A. (2004b). Nonparametric and Semiparametric Models. Springer, New York.
21. HJORT, N. L. and CLAESKENS, G. (2003). Frequentist model average estimators (with discussion). J. Amer. Statist. Assoc. 98 879-945. MR2041481
22. HJORT, N. L. and CLAESKENS, G. (2006). Focussed information criteria and model averaging for Cox's hazard regression model. J. Amer. Statist. Assoc. 101 1449-1464. MR2279471
23. HUANG, J. (1998). Functional ANOVA models for generalized regression. J. Multivariate Anal. 67 49-71. MR1659096
24. HUANG, J. (1999). Efficient estimation of the partly linear additive Cox model. Ann. Statist. 27 1536-1563. MR1742499
25. HUNSBERGER, S. (1994). Semiparametric regression in likelihood-based models. J. Amer. Statist. Assoc. 89 1354-1365. MR1310226
26. HUNSBERGER, S., ALBERT, P., FOLLMANN, D. and SUH, E. (2002). Parametric and semiparametric approaches to testing for seasonal trend in serial count data. Biostatistics 3 289-298.
27. KIM, T. H. andWHITE, H. (2001). James-Stein-type estimators in large samples with application to the least absolute deviations estimator. J. Amer. Statist. Assoc. 96 697-705. MR1946435
28. LEEB, H. and PÖTSCHER, B. M. (2006). Can one estimate the conditional distribution of postmodel- selection estimators? Ann. Statist. 34 2554-2591. MR2291510
29. LEUNG, G. and BARRON, A. R. (2006). Information theory and mixing least-squares regressions. IEEE Trans. Inform. Theory 52 3396-3410. MR2242356
30. LIANG, H. (2008). Generalized partially linear models with missing covariates. J. Multivariate Anal. 99 880-895. MR2405096
31. LIANG, H., THURSTON, S., RUPPERT, D., APANASOVICH, T. and HAUSER, R. (2008). Additive partial linear models with measurement errors. Biometrika 95 667-678.
32. LIN, X. H. and CARROLL, R. J. (2001). Semiparametric regression for clustered data using generalized estimating equations. J. Amer. Statist. Assoc. 96 1045-1056. MR1947252
33. LINTON, O. B. and NIELSEN, J. P. (1995). A kernel method of estimating structured nonparametric regression based on marginal integration. Biometrika 82 93-101. MR1332841
34. MÜLLER, M. and RÖNZ, B. (2000). Credit scoring using semiparametric methods. In Measuring Risk in Complex Stochastic Systems. Lecture Notes in Statistics (J. Franks, W. Härdle and G. Stahl, eds.) 147 83-98. Springer, Berlin.
35. POLLARD, D. (1991). Asymptotics for least absolute deviation regression estimators. Econom. Theory 7 186-199. MR1128411
36. SCHWARZ, G. (1978). Estimating the dimension of a model. Ann. Statist. 6 461-464. MR0468014
37. SEVERINI, T. A. and STANISWALIS, J. G. (1994). Quasi-likelihood estimation in semiparametric models. J. Amer. Statist. Assoc. 89 501-511. MR1294076
38. SHEN, X., HUANG, H. C. andYE, J. (2004). Inference after model selection. J. Amer. Statist. Assoc. 99 751-762. MR2090908
39. SHIBOSKI, C. S. (1998). Generalized additive models for current status data. Lifetime Data Anal. 4 29-50.
40. STONE, C. J. (1986). The dimensionality reduction principle for generalized additive models. Ann. Statist. 14 590-606. MR0840516
41. STONE, C. J. (1994). The use of polynomial spline and their tensor products in multivariate function estimation (with discussion). Ann. Statist. 22 118-184. MR1272079
42. STONE, C. J., HANSEN, M. H., KOOPERBERG, C. and TRUONG, Y. K. (1997). Polynomial splines and their tensor products in extended linear modeling (with discussion). Ann. Statist. 25 1371-1470. MR1463561
43. SUN, J., KOPCIUK, A. K. and LU, X. (2008). Polynomial spline estimation of partially linear single-index proportional hazards regression models. Comput. Statist. Data Anal. 53 176-188. MR2528601
44. VAN DER VAART, A. and WELLNER, J. (1996). Weak Convergence and Empirical Processes. Springer, New York. MR1385671
45. XUE, L. and YANG, L. (2006). Additive coefficient modeling via polynomial spline. Statist. Sinica 16 1423-1446. MR2327498
46. YANG, Y. (2001). Adaptive regression by mixing. J. Amer. Statist. Assoc. 96 574-586. MR1946426
47. YU, K., PARK, B. U. andMAMMEN, E. (2008). Smooth backfitting in generalized additive models. Ann. Statist. 36 228-260. MR2387970