The Accuracy and the Computational Complexity of a Multivariate Binned Kernel Density Estimator

Journal of Multivariate Analysis

Volumn 72, Issue 2, 2000, Pages 264-309

  Holmström, Lasse ^a  

^a UNIVERSITY OF HELSINKI   (Finland)

Author keywords

Binning; Computational complexity; Estimation error; Kernel density estimation

Indexed keywords

EID: 0008923647     PISSN: 0047259X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmva.1999.1863     Document Type: Article

References (23)

1. M. Abramowitz and I. A. Stegun, "Handbook of Mathematical Functions," Dover, New York, NY, 1965.
2. R. A. Adams, "Sobolev Spaces," Academic Press, Orlando, FL, 1975.
3. K. Breuer, "Approximation von Kernglättern durch die WARPing Methode," Diplomarbeit, Fachbereich Statistik, Universität Dortmund, 1990.
4. R. N. Bhattacharya and R. R. Rao, "Normal Approximation and Asymptotic Expansions," Wiley, New York, NY, 1976.
5. P. J. Davis and P. R. Rabinowitz, "Numerical Integration," Blaisdell Publishing Company, Waltham, MA, 1967.
6. L. Devroye, "A Course in Density Estimation," Birkhäuser, Boston, MA, 1987.
7. J. F. Fan and J. S. Marron, Fast implementations of nonparametric curve estimators, J. Comput. Graphical Statist. 3 (1994), 35-56.
8. P. Hall, The influence of rounding errors on some nonparametric estimators of a density and its derivatives, SIAM J. Appl. Math. 42 (1982), 390-399.
9. P. Hall and M. P. Wand, On the accuracy of binned kernel density estimators, J. Multivariate Anal. 56 (1996), 165-184.
10. A. Hämäläinen, Self-organizing map and reduced kernel density estimation, Ph.D. thesis, Research Reports A11, Rolf Nevanlinna Institute, University of Helsinki, 1995.
11. W. K. Härdle and D. W. Scott, Smoothing by weighted averaging of rounded points, Comput. Statist. 7 (1992), 97-128.
12. M. C. Jones, Discretized and interpolated kernel estimates, J. Amer. Statist. Assoc. 84 (1989), 733-741.
13. M. C. Minnotte and D. W. Scott, The mode tree: A tool for visualization of nonparametric density features, J. Comput. Graphical Statist. 2 (1993), 51-68.
14. W. Rudin, "Real and Complex Analysis," McGraw-Hill, New York, NY, second edition, 1974.
15. D. W. Scott, Averaged shifted histograms: effective nonparametric density estimators in several dimensions, Ann. Statist. 13 (1985), 1024-1040.
16. D. W. Scott and S. J. Sheather, Kernel density estimation with binned data, Comm. Statist. Theory Methods 14 (1985), 1353-1359.
17. D. W. Scott, "Multivariate Density Estimation: Theory, Practice, and Visualization," John Wiley & Sons, Inc., New York, NY, 1992.
18. B. W. Silverman, Kernel density estimation using the Fast Fourier Transform. Statistical algorithm AS 176, Appl. Statist. 31 (1982), 93-97.
19. E. M. Stein, "Singular Integrals and Differentiability Properties of Functions," Princeton University Press, Princeton, NJ, 1970.
20. E. M. Stein and G. Weiss, "Fourier Analysis on Euclidean Spaces," Princeton University Press, Princeton, NJ, 1971.
21. F. Szidarovszky and S. Yakowitz, "Principles and Procedures of Numerical Analysis," Plenum Press, New York, NY, 1978.
22. M. P. Wand, Fast computation of multivariate kernel estimators, J. Comput. Graphical Statist. 3 (1994), 433-445.
23. M. P. Wand and M. C. Jones, "Kernel smoothing," Chapman & Hall, London, UK, 1995.