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Volumn 97, Issue 4, 2013, Pages 349-385

Penalized likelihood and Bayesian function selection in regression models

Author keywords

Generalized additive model; Regularization; Smoothing; Spike and slab priors

Indexed keywords


EID: 84884207090     PISSN: 18638171     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10182-013-0211-3     Document Type: Review
Times cited : (24)

References (59)
  • 2
    • 49749090429 scopus 로고    scopus 로고
    • Simultaneous selection of variables and smoothing parameters in structured additive regression models
    • Belitz, C., Lang, S.: Simultaneous selection of variables and smoothing parameters in structured additive regression models. Comput. Stat. Data. Anal. 53, 61-81 (2008).
    • (2008) Comput. Stat. Data. Anal. , vol.53 , pp. 61-81
    • Belitz, C.1    Lang, S.2
  • 4
    • 41549141939 scopus 로고    scopus 로고
    • Boosting algorithms: Regularization, prediction and model fitting
    • Bühlmann, P., Hothorn, T.: Boosting algorithms: Regularization, prediction and model fitting. Stat. Sci. 22, 477-505 (2007).
    • (2007) Stat. Sci. , vol.22 , pp. 477-505
    • Bühlmann, P.1    Hothorn, T.2
  • 5
    • 0043245810 scopus 로고    scopus 로고
    • 2 loss: regression and classification
    • 2 loss: regression and classification. J. Am. Stat. Assoc. 98, 324-339 (2003).
    • (2003) J. Am. Stat. Assoc. , vol.98 , pp. 324-339
    • Bühlmann, P.1    Yu, B.2
  • 6
    • 49549109589 scopus 로고    scopus 로고
    • Variable selection and model averaging in semiparametric overdispersed generalized linear models
    • Cottet, R., Kohn, R. J., Nott, D. J.: Variable selection and model averaging in semiparametric overdispersed generalized linear models. J. Am. Stat. Assoc. 103, 661-671 (2008).
    • (2008) J. Am. Stat. Assoc. , vol.103 , pp. 661-671
    • Cottet, R.1    Kohn, R.J.2    Nott, D.J.3
  • 8
    • 25444532788 scopus 로고    scopus 로고
    • Flexible smoothing using B-splines and penalized likelihood
    • Eilers, P. H. C., Marx, B. D.: Flexible smoothing using B-splines and penalized likelihood. Stat. Sci. 11, 89-121 (1996).
    • (1996) Stat. Sci. , vol.11 , pp. 89-121
    • Eilers, P.H.C.1    Marx, B.D.2
  • 10
    • 84864777167 scopus 로고    scopus 로고
    • Bayesian smoothing and regression for longitudinal, spatial and event history data
    • Fahrmeir, L., Kneib, T.: Bayesian smoothing and regression for longitudinal, spatial and event history data. Oxford Statistical Science Series 36, Oxford (2011).
    • (2011) Oxford Statistical Science Series 36, Oxford
    • Fahrmeir, L.1    Kneib, T.2
  • 11
    • 77953326052 scopus 로고    scopus 로고
    • Bayesian regularization in structured additive regression: a unifying perspective on shrinkage, smoothing and predictor selection
    • Fahrmeir, L., Kneib, T., Konrath, S.: Bayesian regularization in structured additive regression: a unifying perspective on shrinkage, smoothing and predictor selection. Stat. Comput. 20, 203-219 (2010).
    • (2010) Stat. Comput. , vol.20 , pp. 203-219
    • Fahrmeir, L.1    Kneib, T.2    Konrath, S.3
  • 12
    • 1542784498 scopus 로고    scopus 로고
    • Variable selection via nonconcave penalized likelihood and its oracle properties
    • Fan, J., Li, R.: Variable selection via nonconcave penalized likelihood and its oracle properties. J. Am. Stat. Assoc. 96, 1348-1360 (2001).
    • (2001) J. Am. Stat. Assoc. , vol.96 , pp. 1348-1360
    • Fan, J.1    Li, R.2
  • 14
    • 84893179575 scopus 로고
    • Variable selection via Gibbs sampling
    • George, E. I., McCulloch, R. E.: Variable selection via Gibbs sampling. J. Am. Stat. Assoc. 88, 881-889 (1993).
    • (1993) J. Am. Stat. Assoc. , vol.88 , pp. 881-889
    • George, E.I.1    McCulloch, R.E.2
  • 15
    • 0031526204 scopus 로고    scopus 로고
    • Approaches for Bayesian variable selection
    • George, E. I., McCulloch, R. E.: Approaches for Bayesian variable selection. Statistica Sinica 7, 339-374 (1997).
    • (1997) Statistica Sinica , vol.7 , pp. 339-374
    • George, E.I.1    McCulloch, R.E.2
  • 16
    • 67349234649 scopus 로고    scopus 로고
    • Alternative prior distributions for variable selection with very many more variables than observations
    • University of Kent
    • Griffin, J. E., Brown, P. J.: Alternative prior distributions for variable selection with very many more variables than observations. Technical Report UKC/IMS/05/08, IMS, University of Kent (2005).
    • (2005) Technical Report UKC/IMS/05/08, IMS
    • Griffin, J.E.1    Brown, P.J.2
  • 19
    • 77955145935 scopus 로고    scopus 로고
    • Variable selection in nonparametric additive models
    • Huang, J., Horowitz, J. L., Wei, F.: Variable selection in nonparametric additive models. Ann. Stat. 38, 2282-2313 (2010).
    • (2010) Ann. Stat. , vol.38 , pp. 2282-2313
    • Huang, J.1    Horowitz, J.L.2    Wei, F.3
  • 20
    • 22944460748 scopus 로고    scopus 로고
    • Spike and slab variable selection: frequentist and Bayesian strategies
    • Ishwaran, H., Rao, J. S.: Spike and slab variable selection: frequentist and Bayesian strategies. Ann. Stat. 33(2), 730-773 (2005).
    • (2005) Ann. Stat. , vol.33 , Issue.2 , pp. 730-773
    • Ishwaran, H.1    Rao, J.S.2
  • 21
    • 66949120727 scopus 로고    scopus 로고
    • Variable selection and model choice in geoadditive regression models
    • Kneib, T., Hothorn, T., Tutz, G.: Variable selection and model choice in geoadditive regression models. Biometrics 65, 626-634 (2009).
    • (2009) Biometrics , vol.65 , pp. 626-634
    • Kneib, T.1    Hothorn, T.2    Tutz, G.3
  • 22
    • 79952590314 scopus 로고    scopus 로고
    • High-dimensional structured additive regression models: Bayesian regularisation, smoothing and predictive performance
    • Kneib, T., Konrath, S., Fahrmeir, L.: High-dimensional structured additive regression models: Bayesian regularisation, smoothing and predictive performance. Appl. Stat. 60, 51-70 (2011).
    • (2011) Appl. Stat. , vol.60 , pp. 51-70
    • Kneib, T.1    Konrath, S.2    Fahrmeir, L.3
  • 24
    • 34547733991 scopus 로고    scopus 로고
    • Model selection in nonparametric hazard regression
    • Leng, C., Zhang, H. H.: Model selection in nonparametric hazard regression. Nonparametr. Stat. 18, 417-429 (2006).
    • (2006) Nonparametr. Stat. , vol.18 , pp. 417-429
    • Leng, C.1    Zhang, H.H.2
  • 25
    • 33847350805 scopus 로고    scopus 로고
    • Component selection and smoothing in multivariate nonparametric regression
    • Lin, Y., Zhang, H. H.: Component selection and smoothing in multivariate nonparametric regression. Ann. Stat. 34, 2272-2297 (2006).
    • (2006) Ann. Stat. , vol.34 , pp. 2272-2297
    • Lin, Y.1    Zhang, H.H.2
  • 26
    • 79953654016 scopus 로고    scopus 로고
    • Practical variable selection for generalized additive models
    • Marra, G., Wood, S.: Practical variable selection for generalized additive models. Comput. Stat. Data Anal. 55, 2372-2387 (2011).
    • (2011) Comput. Stat. Data Anal. , vol.55 , pp. 2372-2387
    • Marra, G.1    Wood, S.2
  • 27
    • 79956146364 scopus 로고    scopus 로고
    • MATLAB, The MathWorks Inc., Natick, Massachusetts
    • MATLAB. MATLAB version 7. 10. 0 (R2010a). The MathWorks Inc., Natick, Massachusetts (2010).
    • (2010) MATLAB version 7. 10. 0 (R2010a)
  • 30
  • 31
    • 69249230467 scopus 로고    scopus 로고
    • A review of Bayesian variable selection methods: what, how, and which?
    • O'Hara, R. B., Sillanpää, M. J.: A review of Bayesian variable selection methods: what, how, and which? Bayesian Anal. 4, 85-118 (2009).
    • (2009) Bayesian Anal. , vol.4 , pp. 85-118
    • O'Hara, R.B.1    Sillanpää, M.J.2
  • 32
    • 39149101409 scopus 로고    scopus 로고
    • Bayesian identification, selection and estimation of semiparametric functions in high-dimensional additive models
    • Panagiotelis, A., Smith, M.: Bayesian identification, selection and estimation of semiparametric functions in high-dimensional additive models. J. Econom. 143, 291-316 (2008).
    • (2008) J. Econom. , vol.143 , pp. 291-316
    • Panagiotelis, A.1    Smith, M.2
  • 34
    • 84858279402 scopus 로고    scopus 로고
    • Local shrinkage rules, Lévy processes and regularized regression
    • Polson, N. G., Scott, J. G.: Local shrinkage rules, Lévy processes and regularized regression. J. R. Stat. Soc. Ser. B 74(2), 287-311 (2012).
    • (2012) J. R. Stat. Soc. Ser. B , vol.74 , Issue.2 , pp. 287-311
    • Polson, N.G.1    Scott, J.G.2
  • 35
    • 84858341887 scopus 로고    scopus 로고
    • R Development Core Team. R: A Language and Environment for Statistical Computing
    • R Development Core Team. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria (2011). http://www. R-project. org/.
    • (2011) R Foundation for Statistical Computing, Vienna, Austria
  • 36
    • 78651289934 scopus 로고    scopus 로고
    • Variable selection using adaptive nonlinear interaction structures in high dimensions
    • Radchenko, P., James, G. M.: Variable selection using adaptive nonlinear interaction structures in high dimensions. J. Am. Stat. Assoc. 105, 1-13 (2010).
    • (2010) J. Am. Stat. Assoc. , vol.105 , pp. 1-13
    • Radchenko, P.1    James, G.M.2
  • 38
    • 65349194393 scopus 로고    scopus 로고
    • Variable selection in Bayesian smoothing spline ANOVA models: application to deterministic computer codes
    • Reich, B. J., Storlie, C. B., Bondell, H. D.: Variable selection in Bayesian smoothing spline ANOVA models: application to deterministic computer codes. Technometrics 51, 110 (2009).
    • (2009) Technometrics , vol.51 , pp. 110
    • Reich, B.J.1    Storlie, C.B.2    Bondell, H.D.3
  • 41
    • 84884210335 scopus 로고    scopus 로고
    • Mixtures of g-priors for generalised additive model selection with penalised splines
    • University of Zurich and University Bielefeld
    • Sabanés Bové, D., Held, L., Kauermann, G.: Mixtures of g-priors for generalised additive model selection with penalised splines. Technical report, University of Zurich and University Bielefeld (2011). http://arxiv. org/abs/1108. 3520.
    • (2011) Technical report
    • Sabanés, B.D.1    Held, L.2    Kauermann, G.3
  • 43
    • 80052986293 scopus 로고    scopus 로고
    • SpikeSlabGAM: Bayesian variable selection, model choice and regularization for generalized additive mixed models in R
    • 9
    • Scheipl, F.: spikeSlabGAM: Bayesian variable selection, model choice and regularization for generalized additive mixed models in R. Journal of Statistical Software, 43(14), 1-24, 9 (2011b). http://www. jstatsoft. org/v43/i14.
    • (2011) Journal of Statistical Software , vol.43 , Issue.14 , pp. 1-24
    • Scheipl, F.1
  • 44
    • 84871993172 scopus 로고    scopus 로고
    • Spike-and-slab priors for function selection in structured additive regression models
    • Scheipl, F., Fahrmeir, L., Kneib, T.: Spike-and-slab priors for function selection in structured additive regression models. J. Am. Stat. Assoc. 107(500), 1518-1532 (2012). http://arxiv. org/abs/1105. 5250.
    • (2012) J. Am. Stat. Assoc. , vol.107 , Issue.500 , pp. 1518-1532
    • Scheipl, F.1    Fahrmeir, L.2    Kneib, T.3
  • 45
    • 0000824232 scopus 로고    scopus 로고
    • Nonparametric regression using Bayesian variable selection
    • Smith, M., Kohn, R.: Nonparametric regression using Bayesian variable selection. J. Econometr. 75, 317-344 (1996).
    • (1996) J. Econometr. , vol.75 , pp. 317-344
    • Smith, M.1    Kohn, R.2
  • 46
    • 78650732213 scopus 로고    scopus 로고
    • Surface estimation, variable selection, and the nonparametric oracle property
    • Storlie, C., Bondell, H., Reich, B., Zhang, H. H.: Surface estimation, variable selection, and the nonparametric oracle property. Statistica Sinica 21(2), 679-705 (2011).
    • (2011) Statistica Sinica , vol.21 , Issue.2 , pp. 679-705
    • Storlie, C.1    Bondell, H.2    Reich, B.3    Zhang, H.H.4
  • 47
    • 85194972808 scopus 로고    scopus 로고
    • Regression shrinkage and selection via the Lasso
    • Tibshirani, R.: Regression shrinkage and selection via the Lasso. J. R. Stat. Soc. Ser. B 58, 267-288 (1996).
    • (1996) J. R. Stat. Soc. Ser. B , vol.58 , pp. 267-288
    • Tibshirani, R.1
  • 48
    • 33845509035 scopus 로고    scopus 로고
    • Generalized additive modelling with implicit variable selection by likelihood based boosting
    • Tutz, G., Binder, H.: Generalized additive modelling with implicit variable selection by likelihood based boosting. Biometrics 62, 961-971 (2006).
    • (2006) Biometrics , vol.62 , pp. 961-971
    • Tutz, G.1    Binder, H.2
  • 51
    • 34547840186 scopus 로고    scopus 로고
    • Group SCAD regression analysis for microarray time course gene expression data
    • Wang, L., Chen, G., Li, H.: Group SCAD regression analysis for microarray time course gene expression data. Bioinformatics 23, 1486-1494 (2007).
    • (2007) Bioinformatics , vol.23 , pp. 1486-1494
    • Wang, L.1    Chen, G.2    Li, H.3
  • 53
  • 54
    • 70349234037 scopus 로고    scopus 로고
    • Consistent variable selection in additive models
    • Xue, L.: Consistent variable selection in additive models. Statistica Sinica 19, 1281-1296 (2009).
    • (2009) Statistica Sinica , vol.19 , pp. 1281-1296
    • Xue, L.1
  • 55
    • 0037352633 scopus 로고    scopus 로고
    • Bayesian variable selection and model averaging in high-dimensional multinomial nonparametric regression
    • Yau, P., Kohn, R., Wood, S.: Bayesian variable selection and model averaging in high-dimensional multinomial nonparametric regression. J. Comput. Graph. Stat. 12, 23-54 (2003).
    • (2003) J. Comput. Graph. Stat. , vol.12 , pp. 23-54
    • Yau, P.1    Kohn, R.2    Wood, S.3
  • 56
    • 33645035051 scopus 로고    scopus 로고
    • Model selection and estimation in regression with grouped variables
    • Yuan, M., Lin, Y.: Model selection and estimation in regression with grouped variables. J. R. Stat. Soc. Ser. B 68, 49-67 (2006).
    • (2006) J. R. Stat. Soc. Ser. B , vol.68 , pp. 49-67
    • Yuan, M.1    Lin, Y.2
  • 57
    • 80054678826 scopus 로고    scopus 로고
    • Linear or nonlinear? automatic structure discovery for partially linear models
    • Zhang, H. H., Cheng, G., Liu, Y.: Linear or nonlinear? automatic structure discovery for partially linear models. J. Am. Stat. Assoc. 106(495), 1099-1112 (2011).
    • (2011) J. Am. Stat. Assoc , vol.106 , Issue.495 , pp. 1099-1112
    • Zhang, H.H.1    Cheng, G.2    Liu, Y.3
  • 58
    • 33750973351 scopus 로고    scopus 로고
    • Component selection and smoothing for nonparametric regression in exponential families
    • Zhang, H. H., Lin, Y.: Component selection and smoothing for nonparametric regression in exponential families. Statistica Sinica 16, 1021-1041 (2006).
    • (2006) Statistica Sinica , vol.16 , pp. 1021-1041
    • Zhang, H.H.1    Lin, Y.2
  • 59
    • 33846114377 scopus 로고    scopus 로고
    • The adaptive Lasso and its oracle properties
    • Zou, H.: The adaptive Lasso and its oracle properties. J. Am. Stat. Assoc. 101, 1418-1429 (2006).
    • (2006) J. Am. Stat. Assoc. , vol.101 , pp. 1418-1429
    • Zou, H.1


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