On the accuracy of binned kernel density estimators

Journal of Multivariate Analysis

Volumn 56, Issue 2, 1996, Pages 165-184

  Hall, Peter ^a   Wand, M P ^b  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

^b UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

Binning rules; Euler maclaurin summation formulae

Indexed keywords

EID: 0030076590     PISSN: 0047259X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmva.1996.0009     Document Type: Article

References (17)

1. ABRAMOWITZ, M., AND STEGUN, I. A. (1965). Handbook of Mathematical Functions. Dover, New York.
2. FAN, J. AND MARRON, J. S. (1994). Fast implementations of nonparametric curve estimators. J. Comput. Graph. Statist. 3 35-56.
3. GASSER, T., MÜLLER, H.-G., AND MAMMITSZCH, V. (1985). Kernels for nonparametric curve estimation. J. Roy. Statist. Soc. Ser. B. 47 238-252.
4. HALL, P. (1982). The influence of rounding errors on some nonparametric estimators of a density and its derivatives. SIAM J. Appl. Math. 42 390-399.
5. HALL, P. (1983). Edgeworth expansions of the distribution of Stein's statistic. Math. Proc. Cambridge Philos. Soc. 93 163-175.
6. HÄRDLE, W., AND SCOTT D. W. (1992). Smoothing by weighted averaging of rounded points. Comput. Statist. 1 97-128.
7. JONES, M. C. (1989). Discretized and interpolated kernel density estimates. J. Amer. Statist. Assoc. 84 733-741.
8. JONES, M. C., AND LOTWICK, H. W. (1983). On the errors involved in computing the empirical characteristic function. J. Statist. Comput. Simul. 17 133-149.
9. JONES, M. C., AND LOTWICK, H. W. (1984). Remark ASR50. A remark on algorithm AS176. Kernel density estimation using the fast Fourier transform. Appl. Statist. 33 120-122.
10. MARRON J. S., AND WAND, M. P. (1992). Exact mean integrated squared error. Appl. Statist. 20 712-736.
11. MILNE-THOMSON, L. M. (1933). The Calculus of Finite Differences. Macmillan, London.
12. SCOTT, D. W. (1985). Average shifted histograms: Effective nonparametric density estimators in several dimensions. Ann. Statist. 13 1024-1040.
13. SCOTT, D. W. (1992). Multivariate Density Estimation. Wiley, New York.
14. SCOTT, D. W., AND SHEATHER, S. J. (1985). Kernel density estimation with binned data. Comm. Statist. Theory Methods 14 1353-1359.
15. SILVERMAN, B. W. (1982). Kernel density estimation using the fast Fourier transform. Appl. Statist. 31 93-99.
16. SILVERMAN, B. W. (1986). Density Estimation for Statistics and Data Analysis. Chapman Hall, London.
17. WAND, M. P. (1994). Fast computation of multivariate kernel estimators. J. Comput. Graph. Statist. 3 433-445.