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Volumn 41, Issue 4, 2013, Pages 1999-2028

Nonparametric bernstein-von mises theorems in gaussian white noise

Author keywords

Bayesian inference; Efficiency; Plug in property

Indexed keywords


EID: 84907100115     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/13-AOS1133     Document Type: Article
Times cited : (129)

References (40)
  • 2
    • 84871232166 scopus 로고    scopus 로고
    • The semiparametric Bernstein-von Mises theorem
    • MR3013185
    • BICKEL, P. J. andKLEIJN, B. J. K. (2012). The semiparametric Bernstein-von Mises theorem. Ann. Statist. 40 206-237. MR3013185
    • (2012) Ann. Statist. , vol.40 , pp. 206-237
    • Bickel, P.J.1    Kleijn, B.J.K.2
  • 3
    • 0041857920 scopus 로고    scopus 로고
    • Nonparametric estimators which can be "plugged-in."
    • MR2001641
    • BICKEL, P. J. and RITOV, Y. (2003). Nonparametric estimators which can be "plugged-in." Ann. Statist. 31 1033-1053. MR2001641
    • (2003) Ann. Statist. , vol.31 , pp. 1033-1053
    • Bickel, P.J.1    Ritov, Y.2
  • 6
    • 82655181330 scopus 로고    scopus 로고
    • Bernstein-von Mises theorems for Gaussian regression with increasing number of regressors
    • MR2906878
    • BONTEMPS, D. (2011). Bernstein-von Mises theorems for Gaussian regression with increasing number of regressors. Ann. Statist. 39 2557-2584. MR2906878
    • (2011) Ann. Statist. , vol.39 , pp. 2557-2584
    • Bontemps, D.1
  • 7
    • 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
  • 8
    • 84855686993 scopus 로고    scopus 로고
    • A semiparametric Bernstein-von Mises theorem for Gaussian process priors
    • MR2875753
    • CASTILLO, I. (2012). A semiparametric Bernstein-von Mises theorem for Gaussian process priors. Probab. Theory Related Fields 152 53-99. MR2875753
    • (2012) Probab. Theory Related Fields , vol.152 , pp. 53-99
    • Castillo, I.1
  • 9
    • 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
  • 10
    • 0027840161 scopus 로고
    • Wavelets on the interval and fast wavelet transforms
    • MR1256527
    • COHEN, A., DAUBECHIES, I. and VIAL, P. (1993). Wavelets on the interval and fast wavelet transforms. Appl. Comput. Harmon. Anal. 1 54-81. MR1256527
    • (1993) Appl. Comput. Harmon. Anal. , vol.1 , pp. 54-81
    • Cohen, A.1    Daubechies, I.2    Vial, P.3
  • 11
    • 21144475432 scopus 로고
    • An analysis of Bayesian inference for nonparametric regression
    • MR1232525
    • COX, D. D. (1993). An analysis of Bayesian inference for nonparametric regression. Ann. Statist. 21 903-923. MR1232525
    • (1993) Ann. Statist. , vol.21 , pp. 903-923
    • Cox, D.D.1
  • 14
    • 0033236897 scopus 로고    scopus 로고
    • On the Bernstein-von Mises theorem with infinite-dimensional parameters
    • MR1740119
    • FREEDMAN, D. (1999). On the Bernstein-von Mises theorem with infinite-dimensional parameters. Ann. Statist. 27 1119-1140. MR1740119
    • (1999) Ann. Statist. , vol.27 , pp. 1119-1140
    • Freedman, D.1
  • 15
    • 21344494737 scopus 로고
    • Estimating densities of functions of observations
    • MR1294078
    • FREES, E. W. (1994). Estimating densities of functions of observations. J. Amer. Statist. Assoc. 89 517-525. MR1294078
    • (1994) J. Amer. Statist. Assoc. , vol.89 , pp. 517-525
    • Frees, E.W.1
  • 16
    • 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
  • 17
    • 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
  • 18
    • 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
  • 19
    • 49449093584 scopus 로고    scopus 로고
    • Convergence rates of posterior distributions for non-i.I.D. Observations
    • MR2332274
    • GHOSAL, S. and VAN DER VAART, A. (2007). Convergence rates of posterior distributions for non-i.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
  • 20
    • 49749110419 scopus 로고    scopus 로고
    • On local U-statistic processes and the estimation of densities of functions of several sample variables
    • MR2341700
    • GINÉ, E. and MASON, D. M. (2007). On local U-statistic processes and the estimation of densities of functions of several sample variables. Ann. Statist. 35 1105-1145. MR2341700
    • (2007) Ann. Statist. , vol.35 , pp. 1105-1145
    • Giné, E.1    Mason, D.M.2
  • 21
    • 42149093784 scopus 로고    scopus 로고
    • Uniform central limit theorems for kernel density estimators
    • MR2391158
    • GINÉ, E. and NICKL, R. (2008). Uniform central limit theorems for kernel density estimators. Probab. Theory Related Fields 141 333-387. MR2391158
    • (2008) Probab. Theory Related Fields , vol.141 , pp. 333-387
    • Giné, E.1    Nickl, R.2
  • 22
    • 69849086811 scopus 로고    scopus 로고
    • Uniform limit theorems for wavelet density estimators
    • MR2546757
    • GINÉ, E. and NICKL, R. (2009). Uniform limit theorems for wavelet density estimators. Ann. Probab. 37 1605-1646. MR2546757
    • (2009) Ann. Probab. , vol.37 , pp. 1605-1646
    • Giné, E.1    Nickl, R.2
  • 23
    • 84856278451 scopus 로고    scopus 로고
    • r-metrics, 1 ≤ r ≤ ∞
    • MR3012395
    • r-metrics, 1 ≤ r ≤ ∞. Ann. Statist. 39 2883-2911. MR3012395
    • (2011) Ann. Statist. , vol.39 , pp. 2883-2911
    • Giné, E.1    Nickl, R.2
  • 24
    • 0002842430 scopus 로고
    • Asymptotically minimax estimation of concave and convex distribution functions
    • MR0397974
    • KIEFER, J. and WOLFOWITZ, J. (1976). Asymptotically minimax estimation of concave and convex distribution functions. Z. Wahrsch. Verw. Gebiete 34 73-85. MR0397974
    • (1976) Z. Wahrsch. Verw. Gebiete , vol.34 , pp. 73-85
    • Kiefer, J.1    Wolfowitz, J.2
  • 25
    • 84876519489 scopus 로고    scopus 로고
    • Bayesian inverse problems with Gaussian priors
    • MR2906881
    • KNAPIK, B. T., VAN DER VAART, A. W. and VAN ZANTEN, J. H. (2011). Bayesian inverse problems with Gaussian priors. Ann. Statist. 39 2626-2657. MR2906881
    • (2011) Ann. Statist. , vol.39 , pp. 2626-2657
    • Knapik, B.T.1    Van Der Vaart, A.W.2    Van Zanten, J.H.3
  • 26
    • 0002212690 scopus 로고
    • Mémoire sur les formules qui sont fonctions de très grands nombres et sur leurs applications aux probabilités
    • LAPLACE, P. S. (1810). Mémoire sur les formules qui sont fonctions de très grands nombres et sur leurs applications aux probabilités. Oeuvres de Laplace 12 301-345.
    • (1810) Oeuvres de Laplace , vol.12 , pp. 301-345
    • Laplace, P.S.1
  • 27
    • 0030490121 scopus 로고    scopus 로고
    • Efficient estimation of integral functionals of a density
    • MR1394981
    • LAURENT, B. (1996). Efficient estimation of integral functionals of a density. Ann. Statist. 24 659-681. MR1394981
    • (1996) Ann. Statist. , vol.24 , pp. 659-681
    • Laurent, B.1
  • 29
    • 79960986617 scopus 로고    scopus 로고
    • On the Bernstein-von Mises phenomenon in the Gaussian white noise model
    • MR2802048
    • LEAHU, H. (2011). On the Bernstein-von Mises phenomenon in the Gaussian white noise model. Electron. J. Stat. 5 373-404. MR2802048
    • (2011) Electron. J. Stat. , vol.5 , pp. 373-404
    • Leahu, H.1
  • 30
    • 34248222659 scopus 로고    scopus 로고
    • Donsker-type theorems for nonparametric maximum likelihood estimators
    • Correction ibid. 141 331-332
    • NICKL, R. (2007). Donsker-type theorems for nonparametric maximum likelihood estimators. Probab. Theory Related Fields 138 411-449. Correction ibid. 141 331-332.
    • (2007) Probab. Theory Related Fields , vol.138 , pp. 411-449
    • Nickl, R.1
  • 31
    • 58549114383 scopus 로고    scopus 로고
    • On convergence and convolutions of random signed measures
    • MR2472004
    • NICKL, R. (2009). On convergence and convolutions of random signed measures. J. Theoret. Probab. 22 38-56. MR2472004
    • (2009) J. Theoret. Probab. , vol.22 , pp. 38-56
    • Nickl, R.1
  • 32
    • 84872077321 scopus 로고    scopus 로고
    • Bernstein-von Mises theorem for linear functionals of the density
    • MR3015033
    • RIVOIRARD, V. and ROUSSEAU, J. (2012). Bernstein-von Mises theorem for linear functionals of the density. Ann. Statist. 40 1489-1523. MR3015033
    • (2012) Ann. Statist. , vol.40 , pp. 1489-1523
    • Rivoirard, V.1    Rousseau, J.2
  • 33
    • 5644288967 scopus 로고    scopus 로고
    • Root n consistent density estimators for sums of independent random variables
    • MR2094747
    • SCHICK, A. and WEFELMEYER, W. (2004). Root n consistent density estimators for sums of independent random variables. J. Nonparametr. Stat. 16 925-935. MR2094747
    • (2004) J. Nonparametr. Stat. , vol.16 , pp. 925-935
    • Schick, A.1    Wefelmeyer, W.2
  • 34
    • 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
  • 36
    • 51049088387 scopus 로고    scopus 로고
    • Rates of contraction of posterior distributions based on Gaussian process priors
    • MR2418663
    • VAN DER VAART, A. W. and VAN ZANTEN, J. H. (2008). Rates of contraction of posterior distributions based on Gaussian process priors. Ann. Statist. 36 1435-1463. MR2418663
    • (2008) Ann. Statist. , vol.36 , pp. 1435-1463
    • Van Der Vaart, A.W.1    Van Zanten, J.H.2
  • 38
    • 69049092744 scopus 로고    scopus 로고
    • Adaptive Bayesian estimation using a Gaussian random field with inverse gamma bandwidth
    • MR2541442
    • VAN DER VAART, A. W. and VAN ZANTEN, J. H. (2009). Adaptive Bayesian estimation using a Gaussian random field with inverse gamma bandwidth. Ann. Statist. 37 2655-2675. MR2541442
    • (2009) Ann. Statist. , vol.37 , pp. 2655-2675
    • Van Der Vaart, A.W.1    Van Zanten, J.H.2


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