Behaviour of kernel density estimates and bandwidth selectors for contaminated data sets

References

• Billingsley , P. 1968 . Convergence of probability measures. , New York : Wiley .
   Google Scholar
• Bowman , A. W. 1984 . An alternative method of cross-validation for the smoothing of density estimates . Biometrika. , 71 : 353 – 360 .
   Web of Science ®Google Scholar
• Chiu , S. -T. 1991 . The effect of discretization error on bandwidth selection for kernel density estimation . Biometrika , 78 : 436 – 441 .
   Web of Science ®Google Scholar
• Devroye , L. 1989 . On the non-consistency of the L2-cross-validated kernel density estimate . Statist. Probab. Letters , 8 : 425 – 433 .
   Google Scholar
• Grund , B. , Hall , P. and Marron , J. S. 1994 . Loss and risk in smoothing parameter selection . Journal of Nonparametric Statistics , 4 : 107 – 132 .
   Google Scholar
• Hall , P. and Marron , J. S. 1987 . Extent to which least-squares cross-validation minimises integrated squared error in nonparametric density estimation . Probab. Theory Rel. Fields , 74 : 567 – 581 .
   Web of Science ®Google Scholar
• Hall , P. and Marron , J. S. 1991 . Lower bounds for bandwidth selection in density estimation . Probab. Theory Rel. Fields , 90 : 149 – 173 .
   Web of Science ®Google Scholar
• Jong , P. de . 1987 . A central limit theorem for generalized quadratic forms . Probab. Th. Rel. Fields , 75 : 261 – 277 .
   Google Scholar
• Mammen , E. 1992 . When does bootstrap work: asymptotic results and simulations , Vol. 77 , Berlin. New York : Springer Heidelberg . Lecture Notes in. Statistics
   Google Scholar
• Park , B. U. 1989 . On the plug in bandwidth selectors in kernel density estimation . J. Kor. Statist. Soc , 18 : 107 – 117 .
   Google Scholar
• Park , B. U. and Marron , J. S. 1990 . Comparison of data-driven bandwidth selectors . J. Amer. Statist. Assoc. , 85 : 66 – 72 .
   Web of Science ®Google Scholar
• Rudemo , M. 1982 . Empirical choice of histograms and kernel density estimators . Scand. J. Statist. , 9 : 65 – 78 .
   Web of Science ®Google Scholar
• Sheather , S. J. and Jones , M. C. 1991 . A reliable data-based bandwidth selection method for kernel density estimation . Journal of the Royal statistical Society. Series. , B53 : 683 – 690 .
   Google Scholar
• Silverman , B. W. 1986 . Density Estimation for Statistics and Data Analysis , New York : Chapman and Hall .
   Google Scholar
• Van Es , B. 1992 . Asymptotics for least squares cross-validation bandwidths in nonsmooth cases . Ann. Statist , 20 : 1647 – 1657 .
   Web of Science ®Google Scholar
• Woodroofe , M. 1970 . On choosing a delta sequence . Ann. Statist. , 41 : 1665 – 1671 .
   Google Scholar