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Regularization parameter selection for penalized empirical likelihood estimator. (English) Zbl 1417.62187
Summary: Penalized estimation is a useful technique for variable selection when the number of candidate variables is large. A crucial issue in penalized estimation is the selection of the regularization parameter because the performance of the estimator largely depends on an appropriate choice. However, no theoretically sound selection method currently exists for the penalized estimation of moment restriction models. To address this important issue, we develop a novel information criterion, which we call the empirical likelihood information criterion, to select the regularization parameter of the penalized empirical likelihood estimator. The information criterion is derived as an estimator of the expected value of the Kullback-Leibler information criterion from an estimated model to the true data generating process.
62J05 Linear regression; mixed models
62G05 Nonparametric estimation
62B10 Statistical aspects of information-theoretic topics
Full Text: DOI
[1] Akaike, H., Information theory and an extension of the maximum likelihood principle, (Petroc, B.; Csake, F., Second International Symposium on Information Theory, (1973), Akademiai Kiado), 267-281 · Zbl 0283.62006
[2] Andrews, D. W.K.; Lu, B., Consistent model and moment selection procedure for GMM estimation with application to dynamic panel data models, J. Econometrics, 101, 123-164, (2001) · Zbl 0967.62095
[3] Caner, M., Lasso-type GMM estimator, Econometric Theory, 25, 270-290, (2009) · Zbl 1231.62028
[4] Caner, M.; Zhang, H. H., Adaptive elastic net for generalized methods of moments, J. Bus. Econom. Statist., 32, 30-47, (2014)
[5] Chang, J.; Chen, S. X.; Chen, X., High dimensional generalized empirical likelihood for moment restrictions with dependent data, J. Econometrics, 185, 283-304, (2015) · Zbl 1331.62188
[6] Chang, J.; Tang, C. Y.; Wu, T. T., A new scope of penalized empirical likelihood with high-dimensional estimating equations, Ann. Statist., 46, 3185-3216, (2018) · Zbl 1408.62053
[7] Chen, X.; Hong, H.; Shum, M., Nonparametric likelihood ratio model selection tests between parametric likelihood and moment condition models, J. Econometrics, 141, 109-140, (2007) · Zbl 1418.62426
[8] Fan, J.; Li, R., Variable selection via nonconcave penalized likelihood and its oracle properties, J. Amer. Statist. Assoc., 96, 1348-1360, (2001) · Zbl 1073.62547
[9] Gatto, R.; Ronchetti, E., General saddlepoint approximations of marginal densities and tail probabilities, J. Amer. Statist. Assoc., 91, 666-673, (1996) · Zbl 0869.62017
[10] Hannan, E. J.; Quinn, B. G., The determination of the order of an autoregression, J. R. Stat. Soc. Ser. B Stat. Methodol., 41, 190-195, (1979) · Zbl 0408.62076
[11] Hong, H.; Preston, B.; Shum, M., Generalized empirical likelihood-based model selection criteria for moment condition models, Econometric Theory, 19, 923-943, (2003) · Zbl 1441.62735
[12] Hurvich, C. M.; Tsai, C.-L., Regression and time series model selection in small samples, Biometrika, 76, 297-307, (1989) · Zbl 0669.62085
[13] Konishi, S.; Kitagawa, G., Generalised information criteria in model selection, Biometrika, 83, 875-890, (1996) · Zbl 0883.62004
[14] La Vecchia, D.; Ronchetti, E.; Trojani, F., Higher-order infinitesimal robustness, J. Amer. Statist. Assoc., 107, 1546-1557, (2012) · Zbl 1258.62033
[15] Leng, C.; Tang, C. Y., Penalized empirical likelihood and growing dimensional general estimating equations, Biometrika, 99, 703-716, (2012) · Zbl 1437.62522
[16] Öllerer, V.; Croux, C.; Alfons, A., The influence function of penalized regression estimators, Statistics, 49, 741-765, (2015) · Zbl 1328.62481
[17] Qin, J.; Lawless, J., Empirical likelihood and general estimating equations, Ann. Statist., 22, 300-325, (1994) · Zbl 0799.62049
[18] Schwarz, G., Estimating the dimension of a model, Ann. Statist., 6, 461-464, (1978) · Zbl 0379.62005
[19] Shi, Z., Estimation of sparse structral parameter with many endogenous variables, Econometric Rev., 35, 1582-1608, (2016)
[20] Tibshirani, R., Regression shrinkage and selection via the lasso, J. R. Stat. Soc. Ser. B Stat. Methodol., 58, 267-288, (1996) · Zbl 0850.62538
[21] Wang, H.; Li, B.; Leng, C., Shrinkage tuning parameter selection with a diverging number of parameters, J. R. Stat. Soc. Ser. B Stat. Methodol., 71, 671-683, (2009) · Zbl 1250.62036
[22] Zhang, C.-H., Nearly unbiased variable selection under minimax concave penalty, Ann. Statist., 38, 894-942, (2010) · Zbl 1183.62120
[23] Zou, H., The adaptive Lasso and its Oracle properties, J. Amer. Statist. Assoc., 101, 1418-1429, (2006) · Zbl 1171.62326
[24] Zou, H.; Hastie, T., Regularization and variable selection via the elastic net, J. R. Stat. Soc. Ser. B Stat. Methodol., 67, 301-320, (2005) · Zbl 1069.62054
[25] Zou, H.; Hastie, T.; Tibshirani, R., On the “degrees of freedom” of the LASSO, Ann. Statist., 35, 2173-2192, (2007) · Zbl 1126.62061
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