메뉴 건너뛰기




Volumn 39, Issue 5, 2011, Pages 2557-2584

Bernstein-von mises theorems for Gaussian regression with increasing number of regressors

Author keywords

Adaptive estimation; Bernstein von Mises theorem; Nonparametric Bayesian statistics; Posterior asymptotic normality; Semiparametric Bayesian statistics

Indexed keywords


EID: 82655181330     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/11-AOS912     Document Type: Article
Times cited : (53)

References (19)
  • 2
    • 82655164891 scopus 로고    scopus 로고
    • A Bernstein-von Mises theorem for discrete probability distributions
    • MR2471588
    • BOUCHERON, S. and GASSIAT, E. (2009). A Bernstein-von Mises theorem for discrete probability distributions. Electron. J. Stat. 3 114-148. MR2471588
    • (2009) Electron. J. Stat. , vol.3 , pp. 114-148
    • Boucheron, S.1    Gassiat, E.2
  • 3
    • 82655164894 scopus 로고    scopus 로고
    • A semi-parametric Bernstein-von Mises theorem
    • DOI:10.1007/s00440-010-0316-5
    • CASTILLO, I. (2010). A semi-parametric Bernstein-von Mises theorem. Probab. Theory Related Fields. DOI:10.1007/s00440-010-0316-5.
    • (2010) Probab. Theory Related Fields
    • Castillo, I.1
  • 4
    • 0025430804 scopus 로고
    • Information-theoretic asymptotics of Bayes methods
    • MR1053841
    • CLARKE, B. S. and BARRON, A. R. (1990). Information-theoretic asymptotics of Bayes methods. IEEE Trans. Inform. Theory 36 453-471. MR1053841
    • (1990) IEEE Trans. Inform. Theory , vol.36 , pp. 453-471
    • Clarke, B.S.1    Barron, A.R.2
  • 5
    • 84978678945 scopus 로고    scopus 로고
    • Reference priors for exponential families with increasing dimension
    • MR2678969
    • CLARKE, B. and GHOSAL, S. (2010). Reference priors for exponential families with increasing dimension. Electron. J. Stat. 4 737-780. MR2678969
    • (2010) Electron. J. Stat. , vol.4 , pp. 737-780
    • Clarke, B.1    Ghosal, S.2
  • 6
    • 0003363041 scopus 로고
    • A practical guide to splines
    • Springer, New York. MR0507062
    • DE BOOR, C. (1978). A Practical Guide to Splines. Applied Mathematical Sciences 27. Springer, New York. MR0507062
    • (1978) Applied Mathematical Sciences , vol.27
    • De Boor, C.1
  • 7
    • 0033236897 scopus 로고    scopus 로고
    • Wald lecture: On the Bernstein-von Mises theorem with infinitedimensional parameters
    • FREEDMAN, D. (1999). Wald lecture: On the Bernstein-von Mises theorem with infinitedimensional parameters. Ann. Statist. 27 1119-1140.
    • (1999) Ann. Statist. , vol.27 , pp. 1119-1140
    • Freedman, D.1
  • 8
    • 0012224228 scopus 로고    scopus 로고
    • Asymptotic normality of posterior distributions in high-dimensional linear models
    • MR1681701
    • GHOSAL, S. (1999). Asymptotic normality of posterior distributions in high-dimensional linear models. Bernoulli 5 315-331. MR1681701
    • (1999) Bernoulli , vol.5 , pp. 315-331
    • Ghosal, S.1
  • 9
    • 0347117630 scopus 로고    scopus 로고
    • Asymptotic normality of posterior distributions for exponential families when the number of parameters tends to infinity
    • MR1790613
    • GHOSAL, S. (2000). Asymptotic normality of posterior distributions for exponential families when the number of parameters tends to infinity. J. Multivariate Anal. 74 49-68. MR1790613
    • (2000) J. Multivariate Anal. , vol.74 , pp. 49-68
    • Ghosal, S.1
  • 10
    • 0034164796 scopus 로고    scopus 로고
    • Convergence rates of posterior distributions
    • MR1790007
    • GHOSAL, S., GHOSH, J. K. and VAN DER VAART, A. W. (2000). Convergence rates of posterior distributions. Ann. Statist. 28 500-531. MR1790007
    • (2000) Ann. Statist. , vol.28 , pp. 500-531
    • Ghosal, S.1    Ghosh, J.K.2    Van Der Vaart, A.W.3
  • 11
    • 49449093584 scopus 로고    scopus 로고
    • Convergence rates of posterior distributions for noni. i.d. observations
    • MR2332274
    • GHOSAL, S. and VAN DER VAART, A. (2007). Convergence rates of posterior distributions for noni. i.d. observations. Ann. Statist. 35 192-223. MR2332274
    • (2007) Ann. Statist. , vol.35 , pp. 192-223
    • Ghosal, S.1    Van Der Vaart, A.2
  • 12
    • 33845333028 scopus 로고    scopus 로고
    • The bernstein-von Mises theorem for the proportional hazard model
    • DOI 10.1214/009053606000000533
    • KIM, Y. (2006). The Bernstein-von Mises theorem for the proportional hazard model. Ann. Statist. 34 1678-1700. MR2283713 (Pubitemid 44875077)
    • (2006) Annals of Statistics , vol.34 , Issue.4 , pp. 1678-1700
    • Kim, Y.1
  • 13
    • 24344452101 scopus 로고    scopus 로고
    • A Bernstein-von Mises theorem in the nonparametric right-censoring model
    • DOI 10.1214/009053604000000526
    • KIM, Y. and LEE, J. (2004). A Bernstein-von Mises theorem in the nonparametric right-censoring model. Ann. Statist. 32 1492-1512. MR2089131 (Pubitemid 41250274)
    • (2004) Annals of Statistics , vol.32 , Issue.4 , pp. 1492-1512
    • Kim, Y.1    Lee, J.2
  • 14
    • 34247553430 scopus 로고    scopus 로고
    • Concentration inequalities and model selection
    • Springer, Berlin. MR2319879
    • MASSART, P. (2007). Concentration Inequalities and Model Selection. Lecture Notes in Math. 1896. Springer, Berlin. MR2319879
    • (2007) Lecture Notes in Math. , vol.1896
    • Massart, P.1
  • 16
    • 0036489060 scopus 로고    scopus 로고
    • Asymptotic normality of semiparametric and nonparametric posterior distributions
    • MR1947282
    • SHEN, X. (2002). Asymptotic normality of semiparametric and nonparametric posterior distributions. J. Amer. Statist. Assoc. 97 222-235. MR1947282
    • (2002) J. Amer. Statist. Assoc. , vol.97 , pp. 222-235
    • Shen, X.1
  • 17
    • 0035539848 scopus 로고    scopus 로고
    • Rates of convergence of posterior distributions
    • MR1865337
    • SHEN, X. and WASSERMAN, L. (2001). Rates of convergence of posterior distributions. Ann. Statist. 29 687-714. MR1865337
    • (2001) Ann. Statist. , vol.29 , pp. 687-714
    • Shen, X.1    Wasserman, L.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.