메뉴 건너뛰기




Volumn 73, Issue 4, 2011, Pages 601-627

Data-driven density estimation in the presence of additive noise with unknown distribution

Author keywords

Adaptive estimation; Deconvolution; Density estimation; Mean square risk; Minimax rates; Non parametric methods

Indexed keywords


EID: 79961025099     PISSN: 13697412     EISSN: 14679868     Source Type: Journal    
DOI: 10.1111/j.1467-9868.2011.00775.x     Document Type: Article
Times cited : (74)

References (32)
  • 1
    • 0003100694 scopus 로고    scopus 로고
    • From model selection to adaptive estimation
    • In (eds D. Pollard, E. Torgersen and G. L. Yang) New York: Springer.
    • Birgé, L. and Massart, P. (1997) From model selection to adaptive estimation. In Festschrift for Lucien Le Cam (eds D. Pollard, E. Torgersen and G. L. Yang), pp. 55-87. New York: Springer.
    • (1997) Festschrift for Lucien Le Cam , pp. 55-87
    • Birgé, L.1    Massart, P.2
  • 2
    • 3142782035 scopus 로고    scopus 로고
    • Deconvolution of supersmooth densities with smooth noise
    • Butucea, C. (2004) Deconvolution of supersmooth densities with smooth noise. Can. J. Statist., 32, 181-192.
    • (2004) Can. J. Statist. , vol.32 , pp. 181-192
    • Butucea, C.1
  • 3
    • 79961020518 scopus 로고    scopus 로고
    • Sharp optimality in density deconvolution with dominating bias: I
    • Butucea, C. and Tsybakov, A. B. (2007) Sharp optimality in density deconvolution with dominating bias: I. Teor. Veroyatn. Primen., 52, 111-128.
    • (2007) Teor. Veroyatn. Primen. , vol.52 , pp. 111-128
    • Butucea, C.1    Tsybakov, A.B.2
  • 4
    • 0001736196 scopus 로고
    • Optimal rates of convergence for deconvolving a density
    • Carroll, R. J. and Hall, P. (1988) Optimal rates of convergence for deconvolving a density. J. Am. Statist. Ass., 83, 1184-1186.
    • (1988) J. Am. Statist. Ass. , vol.83 , pp. 1184-1186
    • Carroll, R.J.1    Hall, P.2
  • 5
    • 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
  • 6
    • 34248544350 scopus 로고    scopus 로고
    • Wavelet deconvolution with noisy eigenvalues
    • Cavalier, L. and Raimondo, M. (2007) Wavelet deconvolution with noisy eigenvalues. IEEE Trans. Signal Process., 55, 2414-2424.
    • (2007) IEEE Trans. Signal Process. , vol.55 , pp. 2414-2424
    • Cavalier, L.1    Raimondo, M.2
  • 7
    • 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. Can. J. Statist., 34, 431-452.
    • (2006) Can. J. Statist. , vol.34 , pp. 431-452
    • Comte, F.1    Rozenholc, Y.2    Taupin, M.-L.3
  • 8
    • 35649012815 scopus 로고    scopus 로고
    • Finite sample penalization in adaptive density deconvolution
    • Comte, F., Rozenholc, Y. and Taupin, M.-L. (2007) Finite sample penalization in adaptive density deconvolution. J. Statist. Computn Simuln, 77, 977-1000.
    • (2007) J. Statist. Computn Simuln , vol.77 , pp. 977-1000
    • Comte, F.1    Rozenholc, Y.2    Taupin, M.-L.3
  • 9
    • 3142599194 scopus 로고    scopus 로고
    • Bootstrap bandwidth selection in kernel density estimation from a contaminated sample
    • Delaigle, A. and Gijbels, I. (2004) Bootstrap bandwidth selection in kernel density estimation from a contaminated sample. Ann. Inst. Statist. Math., 56, 19-47.
    • (2004) Ann. Inst. Statist. Math. , vol.56 , pp. 19-47
    • Delaigle, A.1    Gijbels, I.2
  • 10
    • 42349113705 scopus 로고    scopus 로고
    • On deconvolution with repeated measurements
    • Delaigle, A., Hall, P. and Meister, A. (2008) On deconvolution with repeated measurements. Ann. Statist., 36, 665-685.
    • (2008) Ann. Statist. , vol.36 , pp. 665-685
    • Delaigle, A.1    Hall, P.2    Meister, A.3
  • 11
    • 84988101319 scopus 로고
    • Consistent deconvolution in density estimation
    • Devroye, L. (1989) Consistent deconvolution in density estimation. Can. J. Statist., 17, 235-239.
    • (1989) Can. J. Statist. , vol.17 , pp. 235-239
    • Devroye, L.1
  • 12
    • 0001095533 scopus 로고
    • A Fourier approach to nonparametric deconvolution of a density estimate
    • Diggle, P. J. and Hall, P. (1993) A Fourier approach to nonparametric deconvolution of a density estimate. J. R. Statist. Soc. B, 55, 523-531.
    • (1993) J. R. Statist. Soc. B , vol.55 , pp. 523-531
    • Diggle, P.J.1    Hall, P.2
  • 13
    • 0031533944 scopus 로고    scopus 로고
    • Density estimation for the case of supersmooth measurement error
    • Efromovich, S. (1997) Density estimation for the case of supersmooth measurement error. J. Am. Statist. Ass., 92, 526-535.
    • (1997) J. Am. Statist. Ass. , vol.92 , pp. 526-535
    • Efromovich, S.1
  • 14
    • 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
  • 16
    • 0011629004 scopus 로고    scopus 로고
    • Data-driven deconvolution
    • Hesse, C. H. (1999) Data-driven deconvolution. J. Nonparam. Statist., 10, 343-373.
    • (1999) J. Nonparam. Statist. , vol.10 , pp. 343-373
    • Hesse, C.H.1
  • 17
    • 44449093772 scopus 로고    scopus 로고
    • Nonlinear estimation for linear inverse problems with error in the operator
    • Hoffmann, M. and Reiss, M. (2008) Nonlinear estimation for linear inverse problems with error in the operator. Ann. Statist., 36, 310-336.
    • (2008) Ann. Statist. , vol.36 , pp. 310-336
    • Hoffmann, M.1    Reiss, M.2
  • 18
    • 69049107546 scopus 로고    scopus 로고
    • Deconvolution with unknown error distribution
    • Johannes, J. (2009) Deconvolution with unknown error distribution. Ann. Statist., 37, 2301-2323.
    • (2009) Ann. Statist. , vol.37 , pp. 2301-2323
    • Johannes, J.1
  • 20
    • 0033240215 scopus 로고    scopus 로고
    • Logspline deconvolution in Besov space
    • Koo, J.-Y. (1999) Logspline deconvolution in Besov space. Scand. J. Statist., 26, 73-86.
    • (1999) Scand. J. Statist. , vol.26 , pp. 73-86
    • Koo, J.-Y.1
  • 21
    • 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. Par., 342, 877-882.
    • (2006) C. R. Math. Acad. Sci. Par. , vol.342 , pp. 877-882
    • Lacour, C.1
  • 22
    • 0011702253 scopus 로고    scopus 로고
    • Nonparametric estimation of the measurement error model using multiple indicators
    • Li, T. and Vuong, Q. (1998) Nonparametric estimation of the measurement error model using multiple indicators. J. Multiv. Anal., 65, 139-165.
    • (1998) J. Multiv. Anal. , vol.65 , pp. 139-165
    • Li, T.1    Vuong, Q.2
  • 23
    • 84988058829 scopus 로고
    • A consistent nonparametric density estimator for the deconvolution problem
    • Liu, M. C. and Taylor, R. L. (1989) A consistent nonparametric density estimator for the deconvolution problem. Can. J. Statist., 17, 427-438.
    • (1989) Can. J. Statist. , vol.17 , pp. 427-438
    • Liu, M.C.1    Taylor, R.L.2
  • 24
    • 0026186424 scopus 로고
    • Multivariate probability density deconvolution for stationary random processes
    • Masry, E. (1991) Multivariate probability density deconvolution for stationary random processes. IEEE Trans. Inform. Theor., 37, 1105-1115.
    • (1991) IEEE Trans. Inform. Theor. , vol.37 , pp. 1105-1115
    • Masry, E.1
  • 25
    • 13244287837 scopus 로고    scopus 로고
    • On the effect of misspecifying the error density in a deconvolution problem
    • Meister, A. (2004) On the effect of misspecifying the error density in a deconvolution problem. Can. J. Statist., 32, 439-449.
    • (2004) Can. J. Statist. , vol.32 , pp. 439-449
    • Meister, A.1
  • 26
    • 0009373055 scopus 로고    scopus 로고
    • On the effect of estimating the error density in nonparametric deconvolution
    • Neumann, M. H. (1997) On the effect of estimating the error density in nonparametric deconvolution. J. Nonparam. Statist., 7, 307-330.
    • (1997) J. Nonparam. Statist. , vol.7 , pp. 307-330
    • Neumann, M.H.1
  • 27
    • 35349001719 scopus 로고    scopus 로고
    • Deconvolution from panel data with unknown error distribution
    • Neumann, M. H. (2007) Deconvolution from panel data with unknown error distribution. J. Multiv. Anal., 98, 1955-1968.
    • (2007) J. Multiv. Anal. , vol.98 , pp. 1955-1968
    • Neumann, M.H.1
  • 28
    • 0345732510 scopus 로고    scopus 로고
    • Removing the effects of additive noise in tirm measurements
    • Odiachi, P. and Prieve, D. (2004) Removing the effects of additive noise in tirm measurements. J. Coll. Interface Sci., 270, 113-122.
    • (2004) J. Coll. Interface Sci. , vol.270 , pp. 113-122
    • Odiachi, P.1    Prieve, D.2
  • 29
    • 0033234633 scopus 로고    scopus 로고
    • Adaptive wavelet estimator for nonparametric density deconvolution
    • Pensky, M. and Vidakovic, B. (1999) Adaptive wavelet estimator for nonparametric density deconvolution. Ann. Statist., 27, 2033-2053.
    • (1999) Ann. Statist. , vol.27 , pp. 2033-2053
    • Pensky, M.1    Vidakovic, B.2
  • 30
    • 84972949113 scopus 로고
    • Deconvoluting kernel density estimators
    • Stefanski, L. and Carroll, R. J. (1990) Deconvoluting kernel density estimators. Statistics, 21, 169-184.
    • (1990) Statistics , vol.21 , pp. 169-184
    • Stefanski, L.1    Carroll, R.J.2
  • 31
    • 0030489977 scopus 로고    scopus 로고
    • New concentration inequalities in product spaces
    • Talagrand, M. (1996) New concentration inequalities in product spaces. Invent. Math., 126, 505-563.
    • (1996) Invent. Math. , vol.126 , pp. 505-563
    • Talagrand, M.1
  • 32
    • 0002055609 scopus 로고
    • Fourier methods for estimating mixing densities and distributions
    • Zhang, C.-H. (1990) Fourier methods for estimating mixing densities and distributions. Ann. Statist., 18, 806-831.
    • (1990) Ann. Statist. , vol.18 , pp. 806-831
    • Zhang, C.-H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.