Frequent problems in calculating integrals and optimizing objective functions: A case study in density deconvolution

Statistics and Computing

Volumn 17, Issue 4, 2007, Pages 349-355

  Delaigle, A ^a,b   Gijbels, I ^c  

^a UNIVERSITY OF BRISTOL   (United Kingdom)

^b UNIVERSITY OF MELBOURNE   (Australia)

^c UNIVERSITY OF LEUVEN   (Belgium)

Author keywords

Bandwidth selection; Dramatic cancellation; Fast Fourier transform; Numerical approximations; Optimization

Indexed keywords

EID: 34548572873     PISSN: 09603174     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11222-007-9024-0     Document Type: Article

References (19)

1. Carroll, R.J., Hall, P.: Optimal rates of convergence for deconvolving a density. J. Am. Stat. Assoc. 83, 1184-1186 (1988)
2. Delaigle, A., Gijbels, I.: Estimation of integrated squared density derivatives from a contaminated sample. J. Roy. Stat. Soc. B 64, 869-886 (2002)
3. Delaigle, A., Gijbels, I.: Bootstrap bandwidth selection in kernel density estimation from a contaminated sample. Ann. Inst. Stat. Math. 56, 19-47 (2004a)
4. Delaigle, A., Gijbels, I.: Practical bandwidth selection in deconvolution kernel density estimation. Comput. Stat. Data Anal. 45, 249-267 (2004b)
5. Delaigle, A., Hall, P.: On the optimal kernel choice for deconvolution. Stat. Probab. Lett. 76, 1594-1602 (2006)
6. Fan, J.: Asymptotic normality for deconvolution kernel density estimators. Sankhya A 53, 97-110 (1991a)
7. Fan, J.: Global behaviour of deconvolution kernel estimates. Stat. Sinica 1, 541-551 (1991b)
8. Fan, J.: On the optimal rates of convergence for nonparametric deconvolution problems. Ann. Stat. 19, 1257-1272 (1991c)
9. Fan, J.: Deconvolution with supersmooth distributions. Can. J. Stat. 20, 155-169 (1992)
10. Hesse, C.H.: Data-driven deconvolution. Nonparametr. Stat. 10, 343-373 (1999)
11. Masry, E.: Asymptotic normality for deconvolution estimators of multivariate densities of stationary processes. J. Multivar. Anal. 44, 47-68 (1993a)
12. Masry, E.: Strong consistency and rates for deconvolution of multivariate densities of stationary processes. Stoch. Process. Appl. 47, 53-74 (1993b)
13. Meister, A.: On the effect of misspecifying the error density in a deconvolution problem. Can. J. Stat. 32, 439-449 (2004)
14. Meister, A.: Density estimation with normal measurement error with unknown variance. Stat. Sinica 16, 195-211 (2006)
15. Press, W.H., Flannery, B.P., Teukolsky, S.A., Vetterling, W.T.: Numerical Recipes in C, The Art of Scientific Computing, 2nd edn. Cambridge University Press, Cambridge (1992)
16. Stefanski, L., Carroll, R.J.: Deconvoluting kernel density estimators. Statistics 2, 169-184 (1990)
17. Van Es, A.J., Uh, H.-W.: Asymptotic normality of kernel type deconvolution estimators: crossing the Cauchy boundary. Nonparametr. Stat. 16, 261-277 (2004)
18. Van Es, A.J., Uh, H.-W.: Asymptotic normality of kernel type deconvolution estimators. Scand. J. Stat. 32, 467-483 (2005)
19. Zhang, S., Karunamuni, R.: Boundary bias correction for nonparametric deconvolution. Ann. Inst. Stat. Math. 52, 612-629 (2000)