Finite sample penalization in adaptive density deconvolution

Journal of Statistical Computation and Simulation

Volumn 77, Issue 11, 2007, Pages 977-1000

  Comte, F ^a   Rozenholc, Y ^a   Taupin, M L ^a  

^a UNIVERSITÉ PARIS DESCARTES   (France)

Author keywords

Adaptive estimation; Data driven; Density deconvolution; Model selection; Penalized contrast; Projection estimator; Simulation study

Indexed keywords

EID: 35649012815     PISSN: 00949655     EISSN: 15635163     Source Type: Journal    
DOI: 10.1080/10629360600831711     Document Type: Article

References (29)

1. Carroll, R.J. and Hall, P., 1988, Optimal rates of convergence for deconvolving a density. Journal of American Statistical Association, 83, 1184-1186.
2. Devroye, L., 1989, Consistent deconvolution in density estimation. Canadian Journal of Statistics, 17, 235-239.
3. Fan, J., 1991, On the optimal rates of convergence for nonparametric deconvolution problem. Annals of Statistics, 19, 1257-1272.
4. Fan, J., 1991, Global behavior of deconvolution kernel estimates. Statistica Sinica, 1, 541-551.
5. Liu, M.C. and Taylor, R.L., 1989, A consistent nonparametric density estimator for the deconvolution problem. Canadian Journal of Statistics, 17, 427-438.
6. Masry, E., 1991, Multivariate probability density deconvolution for stationary random processes. IEEE Transactions on Informations Theory, 37, 1105-1115.
7. Masry, E., 1993, Strong consistency andrates for deconvolution of multivariate densities of stationary processes. Stochastic Processes and their Applications, 47, 53-74.
8. Masry, E., 1993, Asymptotic normality for deconvolution estimators of multivariate densities of stationary processes. Journal of Multivariate Analysis, 44, 47-68.
9. Stefansky, L., 1990, Rates of convergence of some estimators in a class of deconvolution problems. Statistics and Probability Letters, 9, 229-235.
10. Stefansky, L. and Carroll, R.J., 1990, Deconvolution kernel density estimators. Statistics, 21, 169-184.
11. Taylor, R.L. and Zhang, H.M., 1990, On strongly consistent non-parametric density estimator for deconvolution problem. Communications in Statistics Theory and Methods, 19, 3325-3342.
12. Zhang, C.H., 1990, Fourier methods for estimating mixing densities and distributions. Annals of Statistics, 18, 806-831.
13. Cator, E.A., 2001, Deconvolution with arbitrarily smooth kernels. Statistics and Probability Letters, 54, 205-214.
14. Pensky, M. and Vidakovic, B., 1999, Adaptive wavelet estimator for nonparametric density deconvolution. Annals of Statistics, 27(6), 2033-2053.
15. Pensky, M., 2002, Density deconvolution based on wavelets with bounded supports. Statistics and Probability Letters, 56, 261-269.
16. Fan, J. and Koo, J.-Y., 2002, Wavelet deconvolution. IEEE Transactions on Information Theory, 48, 734-747.
17. Butucea, C., 2004, Deconvolution of super smooth densities with smooth noise. Canadian Journal of Statistics, 32, 181-192.
18. Koo, J.-Y., 1999, Logspline deconvolution in Besov space. Scnad. J. Statist., 26, 73-86.
19. Comte, F., Rozenhole, Y. and Taupin, M.-L., 2006, Penalized contrast estimator for density deconvolution. Canadian Journal of Statistics, 34 (to be published).
20. Butucea, C. and Tsybakov, A.B., 2006, Fast asymptotics in density deconvolution. Theory of Probability and its Applications, http://fr.arxiv.org/abs/math.ST/0409471, in press.
21. Delaigle, A. and Gijbels, I., 2004, Practical bandwidth selection in deconvolution kernel density estimation. Computational Statistics and Data Analysis, 45, 249-267.
22. Delaigle, A. and Gijbels, I., 2004, Bootstrap bandwidth selection in kernel density estimation from a contaminated sample. Annals of the Institute of Statistical Mathematics, 56, 19-47.
23. Dalelane, C., 2004, Data driven kernel choice in non-parametric density estimation. Working paper, Technische Universität Braunschweig, Germany.
24. Hesse, C.H., 1999, Data-driven deconvolution. Journal of Nonparametric Statistics, 10, 343-373.
25. Devroye, L., 1986, Nonuniform Random Variate Generation (New-York: Springer-Verlag).
26. Birgé, L. and Rozenholc, Y., 2006, How many bins must be put in a regular histogram. ESAIM Probability and Statistics, 10, 24-45.
27. Comte, F. and Rozenholc, Y., 2004. A new algorithm for fixed design regression and denoising. Annals of the Institute of Statistical Mathematics, 56, 449-473.
28. Bradley, R.C., 1986, Basic properties of strong mixing conditions. In: E. Eberlein and M.S. Taquu (Eds) Dependence in Probability and Statistics. A Survey of Recent Results (Oberwolfar, Birkhäuser). pp. 165-192.
29. Meister, A., 2004, On the effect on misspecifying the error density in deconvolution problem. Canadian Journal of Statistics, 44, 439-450.