×

Generalized predictive information criteria for the analysis of feature events. (English) Zbl 1336.62041

Summary: This paper develops two weighted measures for model selection by generalizing the Kullback-Leibler divergence measure. The concept of a model selection process that takes into account the special features of the underlying model is introduced using weighted measures. New information criteria are defined using the bias correction of an expected weighted loglikelihood estimator. Using weight functions that match the features of interest in the underlying statistical models, the new information criteria are applied to simulated studies of spline regression and copula model selection. Real data applications are also given for predicting the incidence of disease and for quantile modeling of environmental data.

MSC:

62C99 Statistical decision theory
62B10 Statistical aspects of information-theoretic topics
62G08 Nonparametric regression and quantile regression
62P10 Applications of statistics to biology and medical sciences; meta analysis
62P12 Applications of statistics to environmental and related topics
PDFBibTeX XMLCite
Full Text: DOI Euclid

References:

[1] Agostinelli, C. (2002). Robust model selection in regression via weighted likelihood methodology. Statistics & Probability Letters 56 289-300. · Zbl 0998.62034
[2] Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. 2nd Inter. Symp. on Information Theory 267-281. Budapest: Akademiai Kiado. · Zbl 0283.62006
[3] Ando, T. (2007). Bayesian predictive information criterion for the evaluation of hierarchical Bayesian and empirical Bayes models. Biometrika 94 443-458. · Zbl 1132.62005 · doi:10.1093/biomet/asm017
[4] Ando, T. (2012). Predictive Bayesian model selection. American Journal of Mathematical and Management Sciences 31 13-38.
[5] Chen, X and Fan, Y. (2006). Estimation and model selection of semiparametric copula-based multivariate dynamic models under copula misspecification. Journal of Econometrics 135 125-154. · Zbl 1418.62425
[6] Claeskens, G. and Hjort, N. L. (2003). The focused information criterion. Journal of the American Statistical Association 98 900-916. · Zbl 1045.62003 · doi:10.1198/016214503000000819
[7] Efron, B. and Tibshirani, R. J. (1993). An Introduction to the Bootstrap . New York: Chapman and Hall. · Zbl 0835.62038
[8] Eilers, P. H. C. and Marx, B. D. (1996). Flexible smoothing with \(B\)-splines and penalties (with Discussion). Statistical Science 11 89-121. · Zbl 0955.62562
[9] Gronneberg, S. (2010). The copula information criterion and its implications for the maximum pseudo-likelihood estimators. Dependence Modeling 113-138.
[10] Hastie, T., Tibshirani, R. and Friedman, J. (2009). The elements of statistical learning: Data mining, inference, and prediction . New York: Springer. · Zbl 1273.62005
[11] Huard, D., Evin, G. and Favre, A. C. (2006). Bayesian copula selection. Computational Statistics & Data Analysis 51 809-822. · Zbl 1157.62359
[12] Koenker, R. and Xiao, Z. (2006). Quantile autoregression. Journal of the American Statistical Association 101 980-990. · Zbl 1120.62326 · doi:10.1198/016214506000000672
[13] Konishi, S., Ando, T. and Imoto, S. (2004). Bayesian information criteria and smoothing parameter selection in radial basis function networks. Biometrika 91 27-43. · Zbl 1132.62313 · doi:10.1093/biomet/91.1.27
[14] Konishi, S. and Kitagawa, G. (1996). Generalized information criteria in model selection. Biometrika 83 875-890. · Zbl 0883.62004 · doi:10.1093/biomet/83.4.875
[15] Konishi, S. and Kitagawa, G. (2008). Information criteria and statistical modeling . New York: Springer. · Zbl 1172.62003
[16] Kullback, S. and Leibler, R. A. (1951). On information and sufficiency. Annals of Mathematical Statistics 22 79-86. · Zbl 0042.38403 · doi:10.1214/aoms/1177729694
[17] Portnoy, S. and Koenker, R. (1989). Adaptive \(L\) estimation of linear Models. Annals of Statistics 17 362-381. · Zbl 0736.62060 · doi:10.1214/aos/1176347022
[18] Rousseauw, J., du Plessis, J., Benade, A., Jordaan, P., Kotze, J. and Ferreira, J. (1983). Coronary risk factor screening in three rural communities. South African Medical Journal 64 430-436.
[19] Silva, R. S. and Lopes, H. F. (2008). Copula, marginal distributions and model selection: a Bayesian note. Statistics and Computing 18 313-320.
[20] Sin, C. Y. and White, H. (1996). Information criteria for selecting possibly misspecified parametric models. Journal of Econometrics 71 207-225. · Zbl 0843.62089 · doi:10.1016/0304-4076(94)01701-8
[21] Spiegelhalter, D. J., Best, N. G., Carlin, B. P. and van der Linde, A. (2002). Bayesian measures of model complexity and fit (with Discussion). Journal of the Royal Statistical Society, Series B 64 583-639. · Zbl 1067.62010 · doi:10.1111/1467-9868.00353
[22] Takeuchi, K. (1976). Distributions of information statistics and criteria for adequacy of models (in Japanese). Mathematical Science 153 12-18.
[23] Xia, Y. and Tong, H. (2011). Feature matching in time series modeling. Statistical Science 26 21-46. · Zbl 1219.62142 · doi:10.1214/10-STS345
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.