On the existence and limit behavior of the optimal bandwidth for kernel density estimation

Statistica Sinica

Volumn 17, Issue 1, 2007, Pages 289-300

  Chacon J E ^a   Montanero, J ^a   Nogales, A G ^a   Perez P ^a  

^a UNIVERSITY OF EXTREMADURA   (Spain)

Author keywords

Kernel density estimator; Mean integrated squared error; Optimal bandwidth; Sine kernel; Superkernel

Indexed keywords

EID: 34247583880     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (20)

1. Boyd, D. W. and Steele, J. M. (1978). Lower bounds for nonparametric density estimation rates. Ann. Statist. 6, 932-934.
2. Davis, K. B. (1977). Mean integrated square error properties of density estimates. Ann. Statist. 5, 530-535.
3. Devroye, L. (1992). A note on the usefulness of superkernels in density estimation. Ann. Statist. 20, 2037-2056.
4. Devroye, L. and Lugosi, G. (2001). Combinatorial Methods in Density Estimation. Springer-Verlag, New York.
5. Glad, I. K., Hjort, N. L. and Ushakov, N. G. (2003). Correction of density estimators that are not densities. Scand. J. Statist. 30, 415-427.
6. Hall, P. and Marron, J. S. (1991). Lower bounds for bandwidth selection in density estimation. Probab. Theory Related Fields 90, 149-163.
7. Kawata, T. (1972). Fourier Analysis in Probability Theory. Academic Press, New York.
8. Marron, J. S. and Wand, M. P. (1992). Exact mean integrated square error. Ann. Statist. 20, 712-736.
9. Rudin, W. (1990). Fourier Analysis on Groups. Wiley, New York.
10. Sain, S. R. and Scott, D. W. (2002). Zero-bias locally adaptive density estimators. Scand. J. Statist. 29, 441-460.
11. Schucany, W. R. and Sommers, J. P. (1977). Improvement of kernel-type density estimators. J. Amer. Statist. Assoc. 72, 420-423.
12. Scott, D. W. (1992). Multivariate Density Estimation: Theory, Practice and Visualization. Wiley, New York.
13. Sheather, S. J. and Jones, M. C. (1991). A reliable data-based bandwidth selection method for kernel density estimation. J. Roy. Statist. Soc. Ser. B 53, 683-690.
14. Silverman, B. W. (1986). Density Estimation for Statstics and Data Analysis. Chapman and Hall, London.
15. Stone, C. J. (1984). An asymptotically optimal window selection rule for kernel density estimates. Ann. Statist. 12, 1286-1297.
16. van Eeden, C. (1985). Mean integrated squared error of kernel estimators when the density and its derivative are not necessarily continuous. Ann. Inst. Statist. Math. 37, 461-472.
17. van Es, A. J. (1991). Aspects of Nonparametric Density Estimation, CWI Tract 11. CWI, Amsterdam.
18. Wand, M. P. and Jones, M. C. (1995). Kernel Smoothing. Chapman and Hall, London.
19. Wand, M. P. and Schucany, W. R. (1990). Gaussian-based kernels. Canad. J. Statist. 18, 197-204.
20. Yamato, H. (1972). Some statistical properties of estimators of density and distribution functions. Bull. Math. Statist. 15, 113-131.