Relative efficiency of local bandwidths in kernel density estimation^∗

References

• Birgé , L. and Massart , P. 1995 . Estimation of integral ftmctionals of a density . Ann, Statist. , 23 : 11 – 29 .
   Web of Science ®Google Scholar
• Brockmann , M. , Gasser , T. and Herrmann , E. 1993 . Locally adaptive bandwidth choice for kernel regression estimators . Jr. Amer. Statist. Assoc. , 88 : 1302 – 1309 .
   Web of Science ®Google Scholar
• Cao , R. 1990 . Aplicaciones y nuevos resultados del método bootstrap en la estimación no paramétrica de curvas , University of Santiago de Compostela . Ph.D. Dissertation
   Google Scholar
• Cao , R. 1993 . Bootstrapping the mean integrated squared error . Jr. Mult. Anal. , 45 : 137 – 160 .
   Web of Science ®Google Scholar
• Cao , R. , Cuevas , A. and González-Manteiga , W. 1993 . A comparative study of several smoothing methods in density estimation . Comp. Statist. Data Anal. , 17 : 153 – 176 .
   Google Scholar
• Devroye , L. 1997 . Universal smoothing factor selection in density estimation:theory and practice . Test , 6 : 223 – 320 .
   Google Scholar
• Faraway , J. J. and Jhun , M. 1990 . Bootstrap choice of bandwidth for density estimation . Jr. Amer. Statist. Assoc , 85 : 1119 – 1122 .
   Web of Science ®Google Scholar
• Farmen , M. 1996 . The smoothed bootstrap for variable bandwidth selection and some results in nonparametric logistic regression , Chapel Hill : University of North Carolina .
   Google Scholar
• Farmen , M. and Marron , J. S. 1999 . An assessment of finite sample performance of adaptive methods in density estimation . Comp. Statist. Data Anal. , 30 : 143 – 178 .
   Google Scholar
• Hall , P. and Marron , J. S. 1987 . Estimation of integrated squared density derivatives . Statist. Probab. Lett. , 6 : 109 – 115 .
   Web of Science ®Google Scholar
• Hall , P. , Marron , J. S. and Park , B. 1992 . Smoothed cross-validation . Probab. Theor. Rel. Fields , 92 : 1 – 20 .
   Web of Science ®Google Scholar
• Jones , M. C. 1990 . Variable kernel density estimation and variable kernel density estimation . Austral. Jr. Statist. , 4 : 1919 – 1932 .
   Google Scholar
• Jones , M. C. , Marron , J. S. and Sheather , S. J. 1996 . Progress in data-based bandwidth selection for kernel density estimation . Comput. Statist. , 11 : 337 – 381 .
   Web of Science ®Google Scholar
• Jones , M. C. and Sheather , S. J. 1991 . Using non-stochastic terms to advantage in kernel based estimation of integrated squared density derivatives . Statist. Probab. Lett. , 11 : 511 – 514 .
   Web of Science ®Google Scholar
• Loftsgaarden , D. O. and Quesenberry , C. P. 1965 . A nonparametric estimate of a multivariate density function . Ann. Math. Statist. , 36 : 1049 – 1051 .
   Google Scholar
• Marron , J. S. 1992 . Bootstrap bandwidth selection. In:Exploring the limits of the bootstrap , Edited by: LePage , R. and Billard , L. 249 – 262 . New York : John Wiley and Sons .
   Google Scholar
• Marron , J. S. and Wand , M. P. 1992 . Exact mean integrated squared error . Ann. Statist. , 20 : 712 – 736 .
   Web of Science ®Google Scholar
• Rosenblatt , M. 1956 . Remarks on some nonparametric estimate of a density function . Ann. Math. Statist. , 27 : 832 – 837 .
   Google Scholar
• Scott , D. W. 1994 . Multivariate Density Estimation:Theory, Practice and Visualization , New York : Wiley .
   Google Scholar
• Sain , R. S. and Scott , D. W. 1996 . On locally adaptive density estimation . Jr. Amer. Statist. Assoc. , 91 : 1525 – 1534 .
   Web of Science ®Google Scholar
• Sheather , S. J. 1983 . A data-based algorithm for choosing the window width when estimating the density at a point . Comp. Statist. Data Anal. , 1 : 229 – 238 .
   Web of Science ®Google Scholar
• Sheather , S. J. 1986 . An improved data-based algorithm for choosing the window width when estimating the density at a point . Comp. Statist. Data Anal. , 4 : 61 – 65 .
   Web of Science ®Google Scholar
• Sheather , S. J. and Jones , M. C. 1991 . A reliable data-based bandwidth selection method for kernel density estimation . Jr. Royal Statist. Soc. Ser. , B53 : 683 – 690 .
   Google Scholar
• Schucany , W. R. 1995 . Adaptive bandwidth choice for kernel regression . Jr. Amer. Statist. Assoc. , 90 : 535 – 540 .
   Web of Science ®Google Scholar
• Silverman , B. W. 1986 . Density Estimation for Statistics and Data Analysis , London : Chapman and Hall .
   Google Scholar
• Simonoff , J. S. 1996 . Smoothing Methods in Statistics , New York : Springer-Verlag .
   Google Scholar
• Wand , M. P. and Jones , M. C. 1995 . Kernel smoothing , London : Chapman and Hall .
   Google Scholar
• Wu , T.-J. 1995 . Adaptive root n estimates of integrated squared density derivatives . Ann. Statist. , 23 : 1474 – 1495 .
   Web of Science ®Google Scholar