Deconvolution boundary kernel method in nonparametric density estimation

Journal of Statistical Planning and Inference

Volumn 139, Issue 7, 2009, Pages 2269-2283

  Zhang, Shunpu ^a   Karunamuni, Rohana J ^b  

^a UNIVERSITY OF NEBRASKA LINCOLN   (United States)

^b UNIVERSITY OF ALBERTA   (Canada)

Author keywords

Boundary kernel function; Deconvolution; Fourier transformation; Global optimal bandwidth; Nonparametric density estimation

Indexed keywords

EID: 62049083348     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jspi.2008.10.021     Document Type: Article

References (23)

1. Barry J., and Diggle P. Choosing the smoothing parameter in a Fourier approach to nonparametric deconvolution of a density estimate. J. Nonparametric Statist. 4 (1995) 223-232
2. Carroll R.J., and Hall P. Optimal rates of convergence for deconvolving a density. J. Amer. Statist. Assoc. 83 (1988) 1184-1186
3. Delaigle A., and Gijbels I. Estimation of integrated squared density derivatives from a contaminated sample. J. Roy. Statist. Soc. Ser. B 64 (2002) 869-886
4. Delaigle A., and Gijbels I. Comparison on data-driven bandwidth selection procedures in deconvolution kernel density estimation. Comput. Statist. Data Anal. 45 (2003) 249-267
5. Devroye P.L. Consistent deconvolution in density estimation. Canad. J. Statist. 17 (1989) 235-239
6. Diggle P.J., and Hall P. A Fourier approach to nonparametric deconvolution of a density estimate. J. Roy. Statist. Soc. Ser. B 55 (1993) 523-531
7. Fan J. On the optimal rates of convergence for nonparametric deconvolution problems. Ann. Statist. 19 (1991) 1257-1272
8. Fan J. Asymptotic normality for deconvolution kernel density estimators. Sankhya Ser. A 53 (1991) 97-100
9. Fan J. Global behavior of deconvolution kernel estimators. Statist. Sinica 1 (1991) 541-551
10. Fan J. Deconvolution with supersmooth distributions. Canad. J. Statist. 20 (1992) 155-169
11. Gasser T., Müller H.G., and Mammitzsch V. Kernels for nonparametric curve estimation. J. Roy. Statist. Soc. Ser. B 47 (1985) 238-256
12. Karunamuni R.J., and Alberts T. A generalized reflection method of boundary correction in kernel density estimation. Canad. J. Statist. 33 (2005) 497-509
13. Karunamuni R.J., and Alberts T. A locally adaptive transformation method of boundary correction in kernel density estimation. J. Statist. Plann. Inference 136 (2006) 2936-2960
14. Liu M.C., and Taylor R.L. A consistent nonparametric density estimator for the deconvolution problem. Canad. J. Statist. 17 (1989) 427-438
15. Mendelsohn J., and Rice J. Deconvolution of microfluorometric histograms with B splines. J. Amer. Statist. Assoc. 77 (1982) 748-753
16. Stefanski L.A. Rates of convergence of some estimators in a class of deconvolution problems. Statist. Probab. Lett. 9 (1990) 229-235
17. Stefanski L.A., and Carroll R.J. Deconvoluting kernel density estimators. Statistics 21 (1990) 169-184
18. Wand M.P. Finite sample performance of deconvolving density estimators. Statist. Probab. Lett. 37 (1998) 131-139
19. Zhang C.H. Fourier methods for estimating mixing densities and distributions. Ann. Statist. 18 (1990) 806-830
20. Zhang S., and Karunamuni R.J. On kernel density estimation near endpoints. J. Statist. Plann. Inference 70 (1998) 301-316
21. Zhang S., and Karunamuni R.J. On nonparametric density estimation at the boundary. J. Nonparametric Statist. 12 (2000) 197-221
22. Zhang S., and Karunamuni R.J. Boundary bias correction for nonparametric deconvolution. Ann. Inst. Statist. Math. 52 4 (2000) 612-629
23. Zhang S., Karunamuni R.J., and Jones M.C. An improved estimator of the density function at the boundary. J. Amer. Statist. Assoc. 94 (1999) 1231-1241