Estimation of boundary and discontinuity points in deconvolution problems

Statistica Sinica

Volumn 16, Issue 3, 2006, Pages 773-788

  Delaigle, A ^a   Gijbels, I ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF LEUVEN   (Belgium)

Author keywords

Asymptotic distribution; Boundary points; Deconvolution problem; Density estimation; Diagnostic function; Discontinuity points; Endpoints; Rates of convergence

Indexed keywords

EID: 33744973474     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (26)

1. Barry, J. and Diggle, P. (1995). Choosing the smoothing parameter in a Fourier approach to nonparametric deconvolution of a density function. J. Nonparametr. Statist. 4, 223-232.
2. Carroll, R. J. and Hall, P. (1988). Optimal rates of convergence for deconvolving a density. J. Amer. Statist. Assoc. 83, 1184-1186.
3. Chu, C. K. and Cheng, P. E. (1996). Estimation of jump points and jump values of a density function. Statist. Sinica 6, 79-95.
4. Couallier, V. (1999). Estimation non paramétrique d'une discontinuité dans une densité. Comptes Rendus de l'Académie des Sciences, I t.329, 633-636.
5. Couallier, V. (2000). Inference statistique pour des estimateurs de discontinuités dans un cadre non paramétrique. Ph.D. thesis, Laboratoire de Statistique et Probabilités, Université Paul Sabatier, Toulouse III, France.
6. Delaigle, A. (2003). Kernel estimation in deconvolution problems. Ph.D. dissertation. Institut de Statistique, Université Catholique de Louvain, Belgium.
7. Delaigle, A. and Gijbels, I. (2002). Estimation of integrated squared density derivatives from a contaminated sample. J. Roy. Statist. Soc. Ser. B 64, 869-886.
8. Delaigle, A. and Gijbels, I. (2003). Boundary estimation and estimation of discontinuity points in deconvolution problems. Available at http://www.math.ucsd.edu/~adelaigl
9. Delaigle, A. and Gijbels, I. (2004a). Bootstrap bandwidth selection in kernel density estimation from a contaminated sample. Ann. Inst. Statist. Math. 56, 19-47.
10. Delaigle, A. and Gijbels, I. (2004b). Practical bandwidth selection in deconvolution kernel density estimation. Comput. Statist. Data Anal. 45, 249-267.
11. Delaigle, A. and Gijbels, I. (2006). Data-driven boundary estimation in deconvolution problems. Comput. Statist. Data Anal. 50, 1965-1994.
12. Fan, J. (1991a). Asymptotic normality for deconvolution kernel density estimators. Sankhyā Ser. A 53, 97-110.
13. Fan, J. (1991b). Global behaviour of deconvolution kernel estimates. Statist. Sinica 1, 541-551.
14. Fan, J. (1991c). On the optimal rates of convergence for nonparametric deconvolution problems. Ann. Statist. 19, 1257-1272.
15. Gijbels, I. and Goderniaux, A.-C. (2004). Bandwidth selection for change point estimation in nonparametric regression. Technometrics 46, 76-86.
16. Gijbels, I., Hall, P. and Kneip, A. (1999). On the estimation of jump points in smooth curves. Ann. Inst. Statist. Math. 51, 231-251.
17. Goderniaux, A.-C. (2001). Automatic detection of change-points in nonparametric regression. Ph.D. thesis, Institut de Statistique, Université Catholique de Louvain, Belgium.
18. Hall, P. and Simar, L. (2002). Estimating a changepoint, boundary or frontier in the presence of observation error. J. Amer. Statist. Assoc. 97, 523-534.
19. Kneip, A. and Simar, L. (1996). A general framework for frontier estimation with panel data. J. Productivity Anal. 7, 187-212.
20. Li, T. and Vuong, Q. (1998). Nonparametric estimation of the measurement error model using multiple indicators. J. Multivariate Anal. 65, 139-165.
21. Müller, H.-G. (1992). Change-points in noparametric regression analysis. Ann. Statist. 20, 737-761.
22. Neumann, M. H. (1997a). On the effect of estimating the error density in nonparametric deconvolution. J. Nonparametr. Statist. 7, 307-330.
23. Neumann, M. H. (1997b). Optimal change-point estimation in inverse problems. Scand. J. Statist. 24, 503-521.
24. Stefanski, L. and Carroll, R. J. (1990). Deconvoluting kernel density estimators. Statistics 2, 169-184.
25. Wu, J. S. and Chu, C. K. (1993). Kernel-type estimators of jump points and jump values of a regression function. Ann. Statist. 21, 1545-1566.
26. Zhang, S. and Karunamuni, R. (2000). Boundary bias correction for nonparametric deconvolution. Ann. Inst. Statist. Math. 52, 612-629.