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Volumn 123, Issue 2, 2013, Pages 603-628

Posterior consistency via precision operators for Bayesian nonparametric drift estimation in SDEs

Author keywords

Nonparametric Bayesian estimation; Posterior consistency; Stochastic differential equation

Indexed keywords

CONTINUOUS TIME SYSTEMS; DIFFERENTIAL EQUATIONS; STOCHASTIC SYSTEMS;

EID: 84869108779     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spa.2012.08.010     Document Type: Article
Times cited : (53)

References (42)
  • 2
    • 0037273358 scopus 로고    scopus 로고
    • Fully nonparametric estimation of scalar diffusion models
    • F.M. Bandi, P.C.B. Phillips, Fully nonparametric estimation of scalar diffusion models, Econometrica 71 (1) (2003) 241-283.
    • (2003) Econometrica , vol.71 , Issue.1 , pp. 241-283
    • Bandi, F.M.1    Phillips, P.C.B.2
  • 3
    • 0000741389 scopus 로고
    • Nonparametric identification for diffusion processes
    • G. Banon, Nonparametric identification for diffusion processes, SIAM J. Control Optim. 16 (3) (1978) 380-395.
    • (1978) SIAM J. Control Optim , vol.16 , Issue.3 , pp. 380-395
    • Banon, G.1
  • 4
    • 0000473466 scopus 로고
    • A central limit theorem for diffusions with periodic coefficients
    • R. Bhattacharya, A central limit theorem for diffusions with periodic coefficients, Ann. Probab. 13 (2) (1985) 385-396.
    • (1985) Ann. Probab , vol.13 , Issue.2 , pp. 385-396
    • Bhattacharya, R.1
  • 6
    • 84968484311 scopus 로고
    • On the global asymptotic behavior of brownian local time on the circle
    • E. Bolthausen, On the global asymptotic behavior of Brownian local time on the circle, Trans. Amer. Math. Soc. 253 (1979) 317-328.
    • (1979) Trans. Amer. Math. Soc , vol.253 , pp. 317-328
    • Bolthausen, E.1
  • 7
    • 78650708410 scopus 로고    scopus 로고
    • Lower bounds for posterior rates with gaussian process priors
    • I. Castillo, Lower bounds for posterior rates with Gaussian process priors, Electron. J. Stat. 2 (2008) 1281-1299.
    • (2008) Electron. J. Stat , vol.2 , pp. 1281-1299
    • Castillo, I.1
  • 8
    • 47249110597 scopus 로고    scopus 로고
    • Penalized nonparametric mean square estimation of the coefficients of diffusion processes
    • F. Comte, V. Genon-Catalot, Y. Rozenholc, Penalized nonparametric mean square estimation of the coefficients of diffusion processes, Bernoulli 13 (2) (2007) 514-543.
    • (2007) Bernoulli , vol.13 , Issue.2 , pp. 514-543
    • Comte, F.1    Genon-Catalot, V.2    Rozenholc, Y.3
  • 11
    • 0003171807 scopus 로고
    • On the consistency of bayes estimates
    • P. Diaconis, D. Freedman, On the consistency of Bayes estimates, Ann. Statist. 14 (1) (1986) 1-67.
    • (1986) Ann. Statist , vol.14 , Issue.1 , pp. 1-67
    • Diaconis, P.1    Freedman, D.2
  • 14
    • 0034164796 scopus 로고    scopus 로고
    • Convergence rates of posterior distributions
    • S. Ghosal, J.K. Ghosh, A.W. van der Vaart, Convergence rates of posterior distributions, Ann. Statist. 28 (2) (2000) 500-531.
    • (2000) Ann. Statist , vol.28 , Issue.2 , pp. 500-531
    • Ghosal, S.1    Ghosh, J.K.2    Vaart Der Van, A.W.3
  • 15
    • 49449093584 scopus 로고    scopus 로고
    • Convergence rates of posterior distributions for non-i.I.D. Observations
    • S. Ghosal, A.W. van der Vaart, Convergence rates of posterior distributions for non-i.i.d. observations, Ann. Statist. 35 (1) (2007) 192-223.
    • (2007) Ann. Statist , vol.35 , Issue.1 , pp. 192-223
    • Ghosal, S.1    Vaart Der Van, A.W.2
  • 17
    • 52949103277 scopus 로고    scopus 로고
    • Analysis of spdes arising in path sampling, part ii: The nonlinear case
    • M. Hairer, A.M. Stuart, J. Voss, Analysis of SPDEs arising in path sampling, part II: the nonlinear case, Ann. Appl. Probab. 17 (2007) 1657-1706.
    • (2007) Ann. Appl. Probab , vol.17 , pp. 1657-1706
    • Hairer, M.1    Stuart, A.M.2    Voss, J.3
  • 25
    • 69249215134 scopus 로고    scopus 로고
    • Nonparametric bayesian inference for ergodic diffusions
    • L. Panzar, J.H. van Zanten, Nonparametric Bayesian inference for ergodic diffusions, J. Statist. Plann. Inference 139 (12) (2009) 4193-4199.
    • (2009) J. Statist. Plann. Inference , vol.139 , Issue.12 , pp. 4193-4199
    • Panzar, L.1    Van Zanten, J.H.2
  • 26
    • 84865519492 scopus 로고    scopus 로고
    • Nonparametric estimation of diffusions: A differential equations approach
    • O. Papaspiliopoulos, Y. Pokern, G.O. Roberts, A.M. Stuart, Nonparametric estimation of diffusions: a differential equations approach, Biometrika (2012) http://dx.doi.org/10.1093/biomet/ass034.
    • (2012) Biometrika
    • Papaspiliopoulos, O.1    Pokern, Y.2    Roberts, G.O.3    Stuart, A.M.4
  • 31
    • 34250085068 scopus 로고
    • Asymptotic behavior of integral functionals of diffusion processes with periodic coefficients
    • O.A. Safonova, Asymptotic behavior of integral functionals of diffusion processes with periodic coefficients, Ukrainian Math. J. 44 (2) (1992) 215-221.
    • (1992) Ukrainian Math. J , vol.44 , Issue.2 , pp. 215-221
    • Safonova, O.A.1
  • 36
    • 49449112600 scopus 로고    scopus 로고
    • Convergence rates of posterior distributions for brownian semimartingale models
    • F.H. van der Meulen, A.W. van der Vaart, J.H. van Zanten, Convergence rates of posterior distributions for Brownian semimartingale models, Bernoulli 12 (5) (2006) 863-888.
    • (2006) Bernoulli , vol.12 , Issue.5 , pp. 863-888
    • Meulen Der Van, F.H.1    Vaart Der Van, A.W.2    Van Zanten, J.H.3
  • 37
    • 16244414130 scopus 로고    scopus 로고
    • Donsker theorems for diffusions: Necessary and sufficient conditions
    • A.W. van der Vaart, J.H. van Zanten, Donsker theorems for diffusions: necessary and sufficient conditions, Ann. Probab. 33 (4) (2005) 1422-1451.
    • (2005) Ann. Probab , vol.33 , Issue.4 , pp. 1422-1451
    • Vaart Der Van, A.W.1    Van Zanten, J.H.2
  • 38
    • 51049088387 scopus 로고    scopus 로고
    • Rates of contraction of posterior distributions based on gaussian process priors
    • A.W. van der Vaart, J.H. van Zanten, Rates of contraction of posterior distributions based on Gaussian process priors, Ann. Statist. 36 (2008) 1435-1463.
    • (2008) Ann. Statist , vol.36 , pp. 1435-1463
    • Vaart Der Van, A.W.1    Van Zanten, J.H.2
  • 39
    • 69049100661 scopus 로고    scopus 로고
    • Reproducing kernel hilbert spaces of gaussian priors
    • A.W. van der Vaart, J.H. van Zanten, Reproducing Kernel Hilbert spaces of Gaussian priors, IMS Collections 3 (2008) 200-222.
    • (2008) IMS Collections , vol.3 , pp. 200-222
    • Vaart Der Van, A.W.1    Van Zanten, J.H.2
  • 40
    • 0042983816 scopus 로고    scopus 로고
    • Rates of convergence and asymptotic normality of kernel estimators for ergodic diffusion processes
    • J.H. van Zanten, Rates of convergence and asymptotic normality of kernel estimators for ergodic diffusion processes, J. Nonparametr. Stat. 13 (6) (2001) 833-850.
    • (2001) J. Nonparametr. Stat , vol.13 , Issue.6 , pp. 833-850
    • Van Zanten, J.H.1
  • 41
    • 23244446675 scopus 로고    scopus 로고
    • On uniform laws of large numbers for ergodic diffusions and consistency of estimators
    • J.H. van Zanten, On uniform laws of large numbers for ergodic diffusions and consistency of estimators, Stat. Inference Stoch. Process. 6 (2) (2003) 199-213.
    • (2003) Stat. Inference Stoch. Process , vol.6 , Issue.2 , pp. 199-213
    • Van Zanten, J.H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.