Density estimation with normal measurement error with unknown variance

Statistica Sinica

Volumn 16, Issue 1, 2006, Pages 195-211

  Meister, Alexander ^a  

^a UNIVERSITY OF STUTTGART   (Germany)

Author keywords

Deconvolution; Errors in variables; Inversion problems; Nonparametric estimation; Reconstruction

Indexed keywords

EID: 33646404920     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (20)

1. Butucea, C. and Matias, C. (2004). Minimax estimation of the noise level and of the deconvo-lution density in a semiparametric convolution model. To appear in Bernoulli.
2. Carroll, R. J. and Hall, P. (1988). Optimal rates of convergence for deconvolving a density. J. Amer. Statist. Assoc. 83, 1184-1186.
3. Carroll, R. J. and Hall, P. (2004). Low order approximations in deconvolution and regression with errors in variables. J. Roy. Statist. Soc. Ser. B 66, 31-46.
4. Carroll, R. J., Ruppert, D. and Stefanski, L. A. (1995). Measurement Error in Nonlinear Models. Chapman and Hall, London.
5. Delaigle, A. and Gijbels, I. (2004a). Comparison of data-driven bandwidth selection procedures in deconvolution kernel density estimation. Comput. Statist. Data Anal. 45, 249-267.
6. Delaigle, A. and Gijbels, I. (2004b). Bootstrap bandwidth selection in kernel density estimation from a contaminated sample. Ann. Inst. Statist. Math. 56, 19-47.
7. Devroye, L. (1989). Consistent deconvolution in density estimation. Canad. J. Statist. 17, 235-239.
8. Durrett, R. (1996). Probability: theory and examples. 2nd edition. Duxberry Press.
9. Efromovich, S. (1997). Density estimation for the case of supersmooth measurement error. J. Amer. Statist. Assoc. 92, 526-535.
10. Fan, J. (1991). On the optimal rates of convergence for non-parametric deconvolution problems. Ann. Statist. 19, 1257-1272.
11. Fan, J. (1993). Adaptively local one-dimensional subproblems with application to a deconvolution problem. Ann. Statist. 21, 600-610.
12. Hesse, C. H. and Meister, A. (2004). Optimal iterative density deconvolution. J.J. Nonparametr. Stat. 16, 879-900.
13. Hesse, C. H. (1999). Data-driven deconvolution. Journal of Nonparametric Statistics. 10, 343-373.
14. Liu, M. C. and Taylor, R. C. (1989). A consistent nonparametric density estimator for the deconvolution problem. Canad. J. Statist. 17, 427-438.
15. Matias, C. (2002). Semiparametric deconvolution with unknown noise variance. ESAIM. Probab. Stat. 6, 271-292.
16. Meister, A. (2003). Robustheitseigenschaften von Dekonvolutionsdichteschätzern bezüglich Missspezifikation der Fehlerdichte. Dissertation. University of Stuttgart. Germany.
17. Meister, A. (2004a). Deconvolution density estimation with a testing procedure for the error distribution. Technical Report, University of Stuttgart, Germany.
18. Meister, A. (2004b). On the effect of misspecifying the error density in a deconvolution problem. Canad. J. Statist. 32, 439-449.
19. Neumann, M. H. (1997). On the effect of estimating the error density in nonparametric deconvolution. J. Nonparametr. Stat. 7, 307-330.
20. Stefanski, L. A. and Carroll, R. J. (1990). Deconvoluting kernel density estimators. Statistics 21, 169-184.