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Volumn 15, Issue 1, 2009, Pages 69-98

Adaptive estimation of linear functionals in the convolution model and applications

Author keywords

Adaptive density estimation; ARCH models; Deconvolution; Linear functionals; Model selection; Penalized contrast; Stochastic volatility model

Indexed keywords


EID: 62749090971     PISSN: 13507265     EISSN: None     Source Type: Journal    
DOI: 10.3150/08-BEJ146     Document Type: Article
Times cited : (37)

References (29)
  • 2
    • 62749193289 scopus 로고    scopus 로고
    • Adaptive estimation of analytic functions on an interval
    • Artiles Martínez, L.M. and Levit, B.Y. (2003). Adaptive estimation of analytic functions on an interval. Math. Methods Statist. 12 62-94.
    • (2003) Math. Methods Statist , vol.12 , pp. 62-94
    • Artiles Martínez, L.M.1    Levit, B.Y.2
  • 3
    • 84858745362 scopus 로고    scopus 로고
    • Exact adaptive pointwise estimation on Sobolev classes of densities
    • Butucea, C. (2001). Exact adaptive pointwise estimation on Sobolev classes of densities. ESAIM Probab. Statist. 5 1-31.
    • (2001) ESAIM Probab. Statist , vol.5 , pp. 1-31
    • Butucea, C.1
  • 4
    • 3142782035 scopus 로고    scopus 로고
    • Deconvolution of supersmooth densities with smooth noise
    • Butucea, C. (2004). Deconvolution of supersmooth densities with smooth noise. Canad. J. Statist. 32 181-192.
    • (2004) Canad. J. Statist , vol.32 , pp. 181-192
    • Butucea, C.1
  • 5
    • 33845771345 scopus 로고    scopus 로고
    • Exact asymptotics for estimating the marginal density of discretely observed diffusion processes
    • Butucea, C. and Neumann, M.H. (2005). Exact asymptotics for estimating the marginal density of discretely observed diffusion processes. Bernoulli 11 411-444.
    • (2005) Bernoulli , vol.11 , pp. 411-444
    • Butucea, C.1    Neumann, M.H.2
  • 6
    • 42549171048 scopus 로고    scopus 로고
    • Sharp optimality for density deconvolution with dominating bias. I and II
    • Butucea, C. and Tsybakov, A.B. (2007). Sharp optimality for density deconvolution with dominating bias. I and II. Theory Probab. Appl. 52 24-39.
    • (2007) Theory Probab. Appl , vol.52 , pp. 24-39
    • Butucea, C.1    Tsybakov, A.B.2
  • 7
    • 33845608417 scopus 로고    scopus 로고
    • Adaptive estimation of linear functionals under different performance measures
    • Cai, T.T. and Low, M.G. (2005). Adaptive estimation of linear functionals under different performance measures. Bernoulli 11 341-358.
    • (2005) Bernoulli , vol.11 , pp. 341-358
    • Cai, T.T.1    Low, M.G.2
  • 8
    • 28044431578 scopus 로고    scopus 로고
    • On adaptive estimation of linear functionals
    • Cai, T.T. and Low, M.G. (2005). On adaptive estimation of linear functionals. Ann. Statist. 33 2311-2343.
    • (2005) Ann. Statist , vol.33 , pp. 2311-2343
    • Cai, T.T.1    Low, M.G.2
  • 9
    • 0042910589 scopus 로고    scopus 로고
    • Deconvolution with arbitrarily smooth kernels
    • Cator, E.A. (2001). Deconvolution with arbitrarily smooth kernels. Statist. Probab. Lett. 54 205-214.
    • (2001) Statist. Probab. Lett , vol.54 , pp. 205-214
    • Cator, E.A.1
  • 10
    • 0010915732 scopus 로고    scopus 로고
    • On the problem of local adaptive estimation in tomography
    • Cavalier, L. (2001). On the problem of local adaptive estimation in tomography. Bernoulli 7 63-78.
    • (2001) Bernoulli , vol.7 , pp. 63-78
    • Cavalier, L.1
  • 11
    • 33747871988 scopus 로고    scopus 로고
    • Computable infinite-dimensional filters with applications to discretized diffusion processes
    • Chaleyat-Maurel, M. and Genon-Catalot, V. (2006). Computable infinite-dimensional filters with applications to discretized diffusion processes. Stochastic Process. Appl. 116 1447-1467.
    • (2006) Stochastic Process. Appl , vol.116 , pp. 1447-1467
    • Chaleyat-Maurel, M.1    Genon-Catalot, V.2
  • 12
    • 53349163851 scopus 로고    scopus 로고
    • Adaptive density estimation for general ARCH models
    • Comte, F., Dedecker, J. and Taupin, M.-L. (2008). Adaptive density estimation for general ARCH models. Econometric Theory 24 1628-1662.
    • (2008) Econometric Theory , vol.24 , pp. 1628-1662
    • Comte, F.1    Dedecker, J.2    Taupin, M.-L.3
  • 13
    • 33751021665 scopus 로고    scopus 로고
    • Penalized projection estimator for volatility density
    • Comte, F. and Genon-Catalot, V. (2006). Penalized projection estimator for volatility density. Scand. J. Statist. 33 875-893.
    • (2006) Scand. J. Statist , vol.33 , pp. 875-893
    • Comte, F.1    Genon-Catalot, V.2
  • 14
    • 33751016539 scopus 로고    scopus 로고
    • Penalized contrast estimator for adaptive density deconvolution
    • Comte, F., Rozenholc, Y. and Taupin, M.-L. (2006). Penalized contrast estimator for adaptive density deconvolution. Canad. J. Statist. 34 431-452.
    • (2006) Canad. J. Statist , vol.34 , pp. 431-452
    • Comte, F.1    Rozenholc, Y.2    Taupin, M.-L.3
  • 16
    • 0000867838 scopus 로고
    • On the optimal rates of convergence for nonparametric deconvolution problems
    • Fan, J. (1991). On the optimal rates of convergence for nonparametric deconvolution problems. Ann. Statist. 19 1257-1272.
    • (1991) Ann. Statist , vol.19 , pp. 1257-1272
    • Fan, J.1
  • 17
    • 30344458333 scopus 로고    scopus 로고
    • Random scale perturbation of an AR(1) process and its properties as a nonlinear explicit filter
    • Genon-Catalot, V. and Kessler, M. (2004). Random scale perturbation of an AR(1) process and its properties as a nonlinear explicit filter. Bernoulli 10 701-720.
    • (2004) Bernoulli , vol.10 , pp. 701-720
    • Genon-Catalot, V.1    Kessler, M.2
  • 18
    • 0000937636 scopus 로고    scopus 로고
    • On pointwise adaptive nonparametric deconvolution
    • Goldenshluger, A. (1999). On pointwise adaptive nonparametric deconvolution. Bernoulli 5 907-925.
    • (1999) Bernoulli , vol.5 , pp. 907-925
    • Goldenshluger, A.1
  • 19
    • 33747349217 scopus 로고    scopus 로고
    • On adaptive inverse estimation of linear functionals of Hilbert scales
    • Goldenshluger, A. and Pereverzev, S.V. (2003). On adaptive inverse estimation of linear functionals of Hilbert scales. Bernoulli 9 783-807.
    • (2003) Bernoulli , vol.9 , pp. 783-807
    • Goldenshluger, A.1    Pereverzev, S.V.2
  • 20
    • 2542595506 scopus 로고    scopus 로고
    • The method of risk envelopes in the estimation of linear functionals
    • Golubev, G.K. (2004). The method of risk envelopes in the estimation of linear functionals. Problemy Peredachi Informatsii 40 58-72.
    • (2004) Problemy Peredachi Informatsii , vol.40 , pp. 58-72
    • Golubev, G.K.1
  • 21
    • 33845335652 scopus 로고    scopus 로고
    • An oracle approach to adaptive estimation of linear functionals in a Gaussian model
    • Golubev, Y. and Levit, B. (2004). An oracle approach to adaptive estimation of linear functionals in a Gaussian model. Math. Methods Statist. 13 392-408.
    • (2004) Math. Methods Statist , vol.13 , pp. 392-408
    • Golubev, Y.1    Levit, B.2
  • 22
    • 3042813988 scopus 로고    scopus 로고
    • Exact constants for pointwise adaptive estimation under the Riesz transform
    • Klemelä, J. and Tsybakov, A.B. (2004). Exact constants for pointwise adaptive estimation under the Riesz transform. Probab. Theory Related Fields 129 441-467.
    • (2004) Probab. Theory Related Fields , vol.129 , pp. 441-467
    • Klemelä, J.1    Tsybakov, A.B.2
  • 23
    • 33646565990 scopus 로고    scopus 로고
    • Rates of convergence for nonparametric deconvolution
    • Lacour, C. (2006). Rates of convergence for nonparametric deconvolution. C. R. Math. Acad. Sci. Paris 342 877-882.
    • (2006) C. R. Math. Acad. Sci. Paris , vol.342 , pp. 877-882
    • Lacour, C.1
  • 24
    • 62749199944 scopus 로고    scopus 로고
    • Adaptive estimation of linear functionals by model selection
    • Laurent, B., Ludeña, C. and Prieur, C. (2008). Adaptive estimation of linear functionals by model selection. Electron. J. Stat. 2 993-1020.
    • (2008) Electron. J. Stat , vol.2 , pp. 993-1020
    • Laurent, B.1    Ludeña, C.2    Prieur, C.3
  • 25
    • 0000458553 scopus 로고    scopus 로고
    • Adaptive minimax estimation of infinitely differentiable functions
    • Lepski, O.V. and Levit, B.Y. (1998). Adaptive minimax estimation of infinitely differentiable functions. Math. Methods Statist. 7 123-156.
    • (1998) Math. Methods Statist , vol.7 , pp. 123-156
    • Lepski, O.V.1    Levit, B.Y.2
  • 26
    • 0000012624 scopus 로고
    • A problem of adaptive estimation in Gaussian white noise
    • Lepskiǐ, O.V. (1990). A problem of adaptive estimation in Gaussian white noise. Teor. Veroyatnost. i Primenen. 35 459-470.
    • (1990) Teor. Veroyatnost. i Primenen , vol.35 , pp. 459-470
    • Lepskiǐ, O.V.1
  • 28
    • 0032243618 scopus 로고    scopus 로고
    • Pointwise and sup-norm sharp adaptive estimation of functions on the Sobolev classes
    • Tsybakov, A.B. (1998). Pointwise and sup-norm sharp adaptive estimation of functions on the Sobolev classes. Ann. Statist. 26 2420-2469.
    • (1998) Ann. Statist , vol.26 , pp. 2420-2469
    • Tsybakov, A.B.1
  • 29
    • 12444300114 scopus 로고    scopus 로고
    • Nonparametric volatility density estimation for discrete time models
    • Van Es, B., Spreij, P. and van Zanten, H. (2005). Nonparametric volatility density estimation for discrete time models. J. Nonparametr. Statist. 17 237-251.
    • (2005) J. Nonparametr. Statist , vol.17 , pp. 237-251
    • Van Es, B.1    Spreij, P.2    van Zanten, H.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.