Asymptotic normality of the integrated square error of a density estimator in the convolution model

SORT

Volumn 28, Issue 1, 2004, Pages 9-25

  Butucea, C ^a,b  

^a UNIVERSITÉ PARIS OUEST NANTERRE LA DÉFENSE   (France)

^b SORBONNE UNIVERSITÉ   (France)

Author keywords

Central limit theorem; Convolution density estimation; Integrated squared error; Noisy observations; Nonparametric density estimation

Indexed keywords

EID: 3142667676     PISSN: 16962281     EISSN: 20138830     Source Type: Journal    
DOI: None     Document Type: Article

References (10)

1. Butucea, C. (2004). Deconvolution of supersmooth densities with smooth noise, Canadian J. Statist., 32, to appear.
2. Butucea, C. and Tsybakov, A.B. (2003). Fast asymptotics in density deconvolution, Manuscript.
3. Carroll, R.J. and Hall, P. (1988). Optimal rates of convergence for deconvolving a density, J. Amer. Statist. Assoc., 83, 1184-1186.
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5. Fan, J. (1991b). Asymptotic normality for deconvolution kernel density estimators, Sankhyā Ser. A, 53, 97-110.
6. Fan, J. and Koo, J.-Y. (2002). Wavelet deconvolution, IEEE Trans. Inform. Theory, 48, 734-747. (Pubitemid 34239800)
7. Fan, Y. and Liu, Y. (1997). A note on asymtptotic normality for deconvolution kernel estimators, Sankhyā Ser. A, 59, 138-141.
8. Goldenshluger, A. (1999). On pointwise adaptive nonparametric deconvolution, Bernoulli, 5, 907-926.
9. Hall, P. (1984). Central limit theorem for integrated square error of multivariate nonparametric density estimators, Journal of Multivariate Analysis, 14, 1-16.
10. Laurent, B. (1996). Efficient estimation of integral functionals of a density, Ann. Statist., 24, 659-681.