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An improved model averaging scheme for logistic regression. (English) Zbl 1163.62029
Summary: Recently, penalized regression methods have attracted much attention in the statistical literature. We argue that such methods can be improved for the purposes of prediction by utilizing model averaging ideas. We propose a new algorithm that combines penalized regression with model averaging for improved prediction. We also discuss the issue of model selection versus model averaging and propose a diagnostic based on the notion of generalized degrees of freedom. The proposed methods are studied using both simulated and real data.

62G08Nonparametric regression
65C60Computational problems in statistics
62G99Nonparametric inference
Full Text: DOI
[1] Burnham, K. P.; Anderson, D. R.: Model selection and multimodel inference: A practical information-theoretic approach, (2002) · Zbl 1005.62007
[2] Claeskens, G.; Hjort, N. L.: Model selection and model averaging, (2008) · Zbl 1166.62001
[3] Hoerl, A. E.; Kennard, R. W.: Ridge regression: biased estimation for nonorthogonal problems, Technometrics 12, 55-67 (1970) · Zbl 0202.17205 · doi:10.2307/1267351
[4] Tibshirani, R.: Regression shrinkage and selection via the lasso, Journal of the royal statistical society B 58, 267-288 (1996) · Zbl 0850.62538
[5] Fan, J.; Li, R.: Variable selection via nonconcave penalized likelihood and its oracle properties, Journal of the American statistical association 96, 1348-1360 (2001) · Zbl 1073.62547 · doi:10.1198/016214501753382273
[6] Efron, B.; Hastie, T.; Johnstone, T.; Tibshirani, R.: Least angle regression (with discussion), Annals of statistics 32, 407-499 (2004) · Zbl 1091.62054 · doi:10.1214/009053604000000067
[7] Yang, Y.: Adaptive regression by mixing, Journal of American statistical association 96, 574-588 (2001) · Zbl 1018.62033 · doi:10.1198/016214501753168262
[8] Yuan, Z.; Ghosh, D.: Combining logistic regression models for multiple biomarkers, Biometrics 64, 431-439 (2008) · Zbl 1137.62404
[9] Ye, J.: On measuring and correcting the effects of data mining and model selection, Journal of American statistical association 93, 120-131 (1998) · Zbl 0920.62056 · doi:10.2307/2669609
[10] Akaike, H.: Information theory and an extension of the maximum likelihood principle, Proc. 2nd int. Symp. info. Theory, 267-281 (1973) · Zbl 0283.62006
[11] Yuan, Z.; Yang, Y.: Combining linear regression models: when and how?, Journal of American statistical association 100, 1202-1214 (2005) · Zbl 1117.62454 · doi:10.1198/016214505000000088 · http://miranda.asa.catchword.org/vl=689068/cl=11/nw=1/rpsv/cw/asa/01621459/v100n472/s14/p1202
[12] Frank, I. E.; Freidman, J. H.: A statistical view of some chemometrics regression tools, Technometrics 35, 109-148 (1993) · Zbl 0775.62288 · doi:10.2307/1269656
[13] Gibbons, D. G.: A simulation study of some ridge estimators, Journal of the American statistical association 76, 131-139 (1981) · Zbl 0452.62055 · doi:10.2307/2287058
[14] Shen, X.; Huang, H.; Ye, J.: Adaptive model selection and assessment for exponential family distributions, Technometrics 46, 306-317 (2004)
[15] Golub, G. H.; Heath, M.; Wahba, G.: Generalized cross-validation as a method for choosing a good ridge parameter, Technometrics 21, 215-223 (1979) · Zbl 0461.62059 · doi:10.2307/1268518
[16] Barron, A.; Birgé, L.; Massart, P.: Risk bounds for model selection by penalization, Probability theory and related fields 113, 301-413 (1999) · Zbl 0946.62036 · doi:10.1007/s004400050210
[17] Danilov, D.; Magnus, J. R.: On the harm that ignoring pretesting can cause, Journal of econometrics 122, 27-46 (2004) · Zbl 1282.91257
[18] Leeb, H.; Pötscher, B. M.: Can one estimate the conditional distribution of post-model-selection estimators?, Annals of statistics 34, 254-259 (2006) · Zbl 1106.62029 · doi:10.1214/009053606000000821
[19] Leeb, H.; Pötscher, B. M.: Can one estimate the unconditional distribution of post-model-selection estimators?, Econometric theory 24, 338-376 (2008) · Zbl 1284.62152
[20] Hjort, N. L.; Claeskens, G.: Frequentist model average estimators (with discussion), Journal of the American statistical association 98, 879-899 (2003) · Zbl 1047.62003 · doi:10.1198/016214503000000828
[21] Claeskens, G.; Croux, C.; Van Kerckhoven, J.: Variable selection for logistic regression using a prediction focussed information criterion, Biometrics 62, 972-979 (2006) · Zbl 1116.62073 · doi:10.1111/j.1541-0420.2006.00567.x
[22] Obenchain, R. L.: Good and optimal ridge estimators, Annals of statistics 6, 1111-1121 (1978) · Zbl 0384.62059 · doi:10.1214/aos/1176344314
[23] Breiman, L.: Heuristics of instability and stabilization in model selection, The annals of statistics 24, 2350-2383 (1996) · Zbl 0867.62055 · doi:10.1214/aos/1032181158