메뉴 건너뛰기




Volumn 17, Issue 3, 2007, Pages 1065-1090

Adaptive estimation in a nonparametric regression model with errors-in-variables

Author keywords

Adaptive estimation; Density deconvolution; Errors in variables; Minimax estimation; Nonparametric regression; Projection estimators

Indexed keywords


EID: 36249031608     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (11)

References (20)
  • 1
    • 0000492892 scopus 로고    scopus 로고
    • Minimum contrast estimators on sieves: Exponential bounds and rates of convergence
    • Birgé, L. and Massart, P. (1998). Minimum contrast estimators on sieves: exponential bounds and rates of convergence. Bernoulli 4, 329-375.
    • (1998) Bernoulli , vol.4 , pp. 329-375
    • 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. Canadian J. Statist. 32, 181-192
    • (2004) Canadian J. Statist , vol.32 , pp. 181-192
    • Butucea, C.1
  • 3
    • 79961020518 scopus 로고    scopus 로고
    • Sharp optimality for density deconvolution with dominating bias
    • To appear in
    • Butucea, C. and Tsybakov, A.B. (2005). Sharp optimality for density deconvolution with dominating bias. To appear in Theory Probab. Appl., http://fr.arxiv.org/abs/math.ST/0409471.
    • (2005) Theory Probab. Appl
    • Butucea, C.1    Tsybakov, A.B.2
  • 4
    • 84858462921 scopus 로고    scopus 로고
    • Nonparametric estimation of the regression function in an errors-in-variables model
    • Comte, F. and Taupin, M.-L. (2004). Nonparametric estimation of the regression function in an errors-in-variables model. Preprint MAPS 2004-20, http://fr.arxiv.org/abs/math.ST/0511111.
    • (2004) Preprint MAPS , pp. 2004-2020
    • Comte, F.1    Taupin, M.-L.2
  • 5
    • 33751016539 scopus 로고    scopus 로고
    • Penalized contrast estimator for density deconvolution
    • Comte, F., Rozenholc, Y. and Taupin, M.-L. (2006). Penalized contrast estimator for density deconvolution. Canadian J. Statist. 34, 431-452.
    • (2006) Canadian J. Statist , vol.34 , pp. 431-452
    • Comte, F.1    Rozenholc, Y.2    Taupin, M.-L.3
  • 6
    • 36248988632 scopus 로고    scopus 로고
    • Finite sample penalization in adaptive deconvolution
    • To appear in, available online
    • Comte, F., Rozenholc, Y. and Taupin, M.-L. (2005). Finite sample penalization in adaptive deconvolution. To appear in J. Statist. Comput. Simulation, available online.
    • (2005) J. Statist. Comput. Simulation
    • Comte, F.1    Rozenholc, Y.2    Taupin, M.-L.3
  • 7
    • 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
  • 8
    • 38249009969 scopus 로고
    • Multivariate regression estimation with errors-in-variables: Asymptotic normality for mixing processes
    • Fan, J. and Masry, M. (1992). Multivariate regression estimation with errors-in-variables: asymptotic normality for mixing processes. J. Multivariate Anal. 43, 237-272.
    • (1992) J. Multivariate Anal , vol.43 , pp. 237-272
    • Fan, J.1    Masry, M.2
  • 9
    • 21344496605 scopus 로고
    • Nonparametric regression with errors-in-variables
    • Fan, J. and Truong, Y. K. (1993). Nonparametric regression with errors-in-variables. Ann. Statist. 21(4), 1900-1925.
    • (1993) Ann. Statist , vol.21 , Issue.4 , pp. 1900-1925
    • Fan, J.1    Truong, Y.K.2
  • 11
    • 0031566937 scopus 로고    scopus 로고
    • Nonparametric regression with errors in variables and applications
    • Ioannides, D. A. and Alevizos, P. D. (1997). Nonparametric regression with errors in variables and applications. Statist. Probab. Lett. 32, 35-43.
    • (1997) Statist. Probab. Lett , vol.32 , pp. 35-43
    • Ioannides, D.A.1    Alevizos, P.D.2
  • 12
    • 0032165982 scopus 로고    scopus 로고
    • B-spline estimation of regression functions with errors in variable
    • Koo, J.-Y. and Lee K.-W. (1998). B-spline estimation of regression functions with errors in variable. Statist. Probab. Lett. 40, 57-66.
    • (1998) Statist. Probab. Lett , vol.40 , pp. 57-66
    • Koo, J.-Y.1    Lee, K.-W.2
  • 13
    • 84996133877 scopus 로고    scopus 로고
    • On Talagrand's deviation inequalities for product measures
    • Ledoux, M. (1996). On Talagrand's deviation inequalities for product measures. ESAIM Probab. Statist, 63-87.
    • (1996) ESAIM Probab. Statist , pp. 63-87
    • Ledoux, M.1
  • 14
    • 0003009222 scopus 로고
    • Multivariate regression estimation with errors-in-variables for stationary processes
    • Masry, E. (1993), Multivariate regression estimation with errors-in-variables for stationary processes. J. Nonparametr. Statist. 3, 13-36.
    • (1993) J. Nonparametr. Statist , vol.3 , pp. 13-36
    • Masry, E.1
  • 15
    • 84858471420 scopus 로고    scopus 로고
    • Meyer, E. (1990). Ondelettes et opérateurs. I., Ondelettes, Actualités Mathématiques. (Wavelets and operators. I., Wavelets, Current Mathematical Topics), Hermann, Paris.
    • Meyer, E. (1990). Ondelettes et opérateurs. I., Ondelettes, Actualités Mathématiques. (Wavelets and operators. I., Wavelets, Current Mathematical Topics), Hermann, Paris.
  • 16
    • 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
  • 17
    • 51249187914 scopus 로고
    • p, (p > 2), spanned by sequences of independent random variables
    • p, (p > 2), spanned by sequences of independent random variables. Israel J. Math. 8, 273-303.
    • (1970) Israel J. Math , vol.8 , pp. 273-303
    • Rosenthal, H.P.1
  • 18
    • 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
  • 19
    • 0010886029 scopus 로고
    • Nonparametric curve estimation with time series errors
    • Truong, Y. K. (1991). Nonparametric curve estimation with time series errors. J. Statist Plann Inference 28, 167-183.
    • (1991) J. Statist Plann Inference , vol.28 , pp. 167-183
    • Truong, Y.K.1
  • 20
    • 0022692335 scopus 로고
    • Robust reconstruction of functions by the local-approximation method
    • Tsybakov, A. B. (1986). Robust reconstruction of functions by the local-approximation method. Probl. Inf. Transm. 22, 133-146.
    • (1986) Probl. Inf. Transm , vol.22 , pp. 133-146
    • Tsybakov, A.B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.