메뉴 건너뛰기




Volumn 7, Issue 2, 2012, Pages 477-502

Regularization in regression: Comparing Bayesian and frequentist methods in a poorly informative situation

Author keywords

Calibration; Dantzig selector; Elastic net; Lasso; Model choice; Noninformative priors; Regularization methods; Zellner's g prior

Indexed keywords


EID: 84865715409     PISSN: 19360975     EISSN: 19316690     Source Type: Journal    
DOI: 10.1214/12-BA716     Document Type: Article
Times cited : (44)

References (44)
  • 1
    • 0000609589 scopus 로고
    • A comment on D.V. Lindley's statistical paradox
    • Bartlett, M. (1957). A comment on D.V. Lindley's statistical paradox. Biometrika, 44:533-534.
    • (1957) Biometrika , vol.44 , pp. 533-534
    • Bartlett, M.1
  • 2
    • 0001505281 scopus 로고    scopus 로고
    • Bayes factors and marginal distributions in invariant situations
    • Berger, J., Pericchi, L., and Varshavsky, I. (1998). Bayes factors and marginal distributions in invariant situations. Sankhya A, 60:307-321.
    • (1998) Sankhya A , vol.60 , pp. 307-321
    • Berger, J.1    Pericchi, L.2    Varshavsky, I.3
  • 3
    • 79951540621 scopus 로고    scopus 로고
    • Evolutionary stochastic search for Bayesian model exploration
    • Bottolo, L. and Richardson, S. (2010). Evolutionary stochastic search for Bayesian model exploration. Bayesian Analysis, 5(3):583-618.
    • (2010) Bayesian Analysis , vol.5 , Issue.3 , pp. 583-618
    • Bottolo, L.1    Richardson, S.2
  • 4
    • 84950771789 scopus 로고
    • Estimating optimal transformations for multiple regression and correlation
    • Breiman, L. and Friedman, J.H. (1985). Estimating optimal transformations for multiple regression and correlation. Journal of the American Statistical Association, 85(391):580-598.
    • (1985) Journal of the American Statistical Association , vol.85 , Issue.391 , pp. 580-598
    • Breiman, L.1    Friedman, J.H.2
  • 6
    • 0036389689 scopus 로고    scopus 로고
    • Laplace approximations for hypergeometric functions with matrix arguments
    • Butler, R. and Wood, A. (2002). Laplace approximations for hypergeometric functions with matrix arguments. Annals of Statistics, 30:1155-1177.
    • (2002) Annals of Statistics , vol.30 , pp. 1155-1177
    • Butler, R.1    Wood, A.2
  • 7
    • 34548275795 scopus 로고    scopus 로고
    • The Dantzig Selector, statistical estimation when p is much larger than n
    • Candes, E. and Tao, T. (2007). The Dantzig Selector: statistical estimation when p is much larger than n. Annals of Statistics, 35(6):2313-2351.
    • (2007) Annals of Statistics , vol.35 , Issue.6 , pp. 2313-2351
    • Candes, E.1    Tao, T.2
  • 10
    • 0030532505 scopus 로고    scopus 로고
    • Bayesian variable selection with related predictors
    • Chipman, H. (1996). Bayesian variable selection with related predictors. Canadian Journal of Statistics, 1:17-36.
    • (1996) Canadian Journal of Statistics , vol.1 , pp. 17-36
    • Chipman, H.1
  • 13
    • 84950615108 scopus 로고
    • Doingwhat comes naturally, Interpreting a tail area as a posterior probability or as a likelihood ratio
    • DeGroot, M. (1973). Doing what comes naturally: Interpreting a tail area as a posterior probability or as a likelihood ratio. Journal of the American Statistical Association, 68:966-969.
    • (1973) Journal of the American Statistical Association , vol.68 , pp. 966-969
    • DeGroot, M.1
  • 14
    • 0037290186 scopus 로고    scopus 로고
    • Bayesian variable selection in qualitative models by Kullback-Leibler projections
    • Dupuis, J. and Robert, C. (2003). Bayesian variable selection in qualitative models by Kullback-Leibler projections. Journal of Statistical Planning and Inference, 111:77-94.
    • (2003) Journal of Statistical Planning and Inference , vol.111 , pp. 77-94
    • Dupuis, J.1    Robert, C.2
  • 15
    • 18044404766 scopus 로고    scopus 로고
    • Benchmark priors for Bayesian model averaging
    • Fernandez, C., Ley, E., and Steel, M. (2001). Benchmark priors for Bayesian model averaging. Journal of Econometrics, 100:381-427.
    • (2001) Journal of Econometrics , vol.100 , pp. 381-427
    • Fernandez, C.1    Ley, E.2    Steel, M.3
  • 16
    • 21844523862 scopus 로고
    • The risk ination criterion for multiple regression
    • Foster, D. and George, E. (1994). The risk ination criterion for multiple regression. Annals of Statistics, 22:1947-1975.
    • (1994) Annals of Statistics , vol.22 , pp. 1947-1975
    • Foster, D.1    George, E.2
  • 18
    • 0001729472 scopus 로고    scopus 로고
    • Calibration and empirical Bayes variable selection
    • George, E. and Foster, D. (2000). Calibration and empirical Bayes variable selection. Biometrika, 87(4):731-747.
    • (2000) Biometrika , vol.87 , Issue.4 , pp. 731-747
    • George, E.1    Foster, D.2
  • 20
    • 0031526204 scopus 로고    scopus 로고
    • Approaches to Bayesian variable selection
    • George, E. and McCulloch, R. (1997). Approaches to Bayesian variable selection. Sta-tistica Sinica, 7:339-373.
    • (1997) Sta-tistica Sinica , vol.7 , pp. 339-373
    • George, E.1    McCulloch, R.2
  • 21
    • 84857650851 scopus 로고    scopus 로고
    • Bayes factor consistency in linear models
    • Philadelphia, June 5-9, 2009
    • Guo, R. and Speckman, P. (2009). Bayes factor consistency in linear models. In The 2009 International Workshop on Objective Bayes Methodology, Philadelphia, June 5-9, 2009. URL http://www-stat.wharton.upenn.edu/statweb/Conference/ OBayes09/AbstractPapers/speckman.pdf.
    • (2009) The 2009 International Workshop on Objective Bayes Methodology
    • Guo, R.1    Speckman, P.2
  • 22
    • 84942484786 scopus 로고
    • Ridge regression, biased estimation for non orthogonal problems
    • Hoerl, A. and Kennard, R. (1970). Ridge regression: biased estimation for non orthogonal problems. Technometrics, 12:55-67.
    • (1970) Technometrics , vol.12 , pp. 55-67
    • Hoerl, A.1    Kennard, R.2
  • 24
    • 27944462549 scopus 로고
    • A reference Bayesian test for nested hypotheses and its relationship to the Schwarz criterion
    • Kass, R. and Wasserman, L. (1995). A reference Bayesian test for nested hypotheses and its relationship to the Schwarz criterion. Journal of the American Statistical Association, 90:928-934.
    • (1995) Journal of the American Statistical Association , vol.90 , pp. 928-934
    • Kass, R.1    Wasserman, L.2
  • 25
    • 0010081155 scopus 로고    scopus 로고
    • Nonparametric regression using linear combinations of basis functions
    • Kohn, R., Smith, M., and Chan, D. (2001). Nonparametric regression using linear combinations of basis functions. Statistics and Computing, 11:313-322.
    • (2001) Statistics and Computing , vol.11 , pp. 313-322
    • Kohn, R.1    Smith, M.2    Chan, D.3
  • 27
    • 0000810338 scopus 로고
    • A statistical paradox
    • Lindley, D. (1957). A statistical paradox. Biometrika, 44:187-192.
    • (1957) Biometrika , vol.44 , pp. 187-192
    • Lindley, D.1
  • 32
    • 0042622454 scopus 로고
    • Generalized body composition prediction equation for men using simple measurement techniques
    • Penrose, K., Nelson, A., and Fisher, A. (1985). Generalized body composition prediction equation for men using simple measurement techniques. Medicine and Science in Sports and Exercise, 17(2):189.
    • (1985) Medicine and Science in Sports and Exercise , vol.17 , Issue.2 , pp. 189
    • Penrose, K.1    Nelson, A.2    Fisher, A.3
  • 35
    • 0011890988 scopus 로고
    • A note on the Jeffreys-Lindley paradox
    • Robert, C. (1993). A note on the Je_reys-Lindley paradox. Statistica Sinica, 3:601-608.
    • (1993) Statistica Sinica , vol.3 , pp. 601-608
    • Robert, C.1
  • 37
    • 4444220247 scopus 로고    scopus 로고
    • Perfect sampling for Bayesian variable selection in a linear regression model
    • Schneider, U. and Corcoran, J. (2004). Perfect sampling for Bayesian variable selection in a linear regression model. Journal of Statistical Planning and Inference, 126:153-171.
    • (2004) Journal of Statistical Planning and Inference , vol.126 , pp. 153-171
    • Schneider, U.1    Corcoran, J.2
  • 38
    • 0000824232 scopus 로고    scopus 로고
    • Nonparametric regression using Bayesian variable selection
    • Smith, M. and Kohn, R. (1996). Nonparametric regression using Bayesian variable selection. Journal of Econometrics, 75:317-343.
    • (1996) Journal of Econometrics , vol.75 , pp. 317-343
    • Smith, M.1    Kohn, R.2
  • 40
    • 33645035051 scopus 로고    scopus 로고
    • Model selection and estimation in regression with grouped variables
    • Yuan, M. and Lin, Y. (2007). Model selection and estimation in regression with grouped variables. Journal of the Royal Statistical Society Series B, 68(1):49-67.
    • (2007) Journal of the Royal Statistical Society Series B , vol.68 , Issue.1 , pp. 49-67
    • Yuan, M.1    Lin, Y.2
  • 41
    • 0002817906 scopus 로고
    • On assessing prior distributions and Bayesian regression analysis with g-prior distribution regression using Bayesian variable selection
    • North-Holland / Elsevier
    • Zellner, A. (1986). On assessing prior distributions and Bayesian regression analysis with g-prior distribution regression using Bayesian variable selection. In Bayesian inference and decision techniques: Essays in Honor of Bruno De Finetti, pages 233-243. North-Holland / Elsevier.
    • (1986) Bayesian inference and decision techniques, Essays in Honor of Bruno De Finetti , pp. 233-243
    • Zellner, A.1
  • 42
    • 0039026915 scopus 로고
    • Posterior odds ratios for selected regression hypotheses
    • Valencia, University Press. (Proceedings of the first Valencia meeting)
    • Zellner, A. and Siow, A. (1980). Posterior odds ratios for selected regression hypotheses. In Bayesian Statistics, pages 585-603. Valencia: University Press. (Proceedings of the first Valencia meeting).
    • (1980) Bayesian Statistics , pp. 585-603
    • Zellner, A.1    Siow, A.2
  • 44
    • 16244401458 scopus 로고    scopus 로고
    • Regularization and variable selection via the elastic net
    • Zou, H. and Hastie, T. (2005). Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society Series B, 67(2):301-320. 478, 484, 485
    • (2005) Journal of the Royal Statistical Society Series B , vol.67 , Issue.2 , pp. 301-320
    • Zou, H.1    Hastie, T.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.