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DENSITY ESTIMATION 597 HALL,P.and MARRON,J.S.(1987b).Estimation of integrated SCOTT,D.W.and TERRELL,G.R.(1987).Biased and unbiased squared density derivatives.Statist.Probab.Lett.6109-115. cross-validation in density estimation.J.Amer:Statist.Assoc HALL,P.and MARRON,J.S.(1991).Local minima in cross- 821131-1146. validation functions.J.Roy.Statist.Soc.Ser:B 53 245-252. SEGAL,M.R.and WIEMELS,J.L.(2002).Clustering of translo- HALL,P.and MINNOTTE,M.C.(2002).Higher order data sharp- cation breakpoints.J.Amer:Statist.Assoc.97 66-76. ening for density estimation.J.R.Stat.Soc.Ser:B Stat. SHEATHER,S.J.(1992).The performance of six popular band- Methodol.64 141-157. width selection methods on some real data sets (with discus- HALL,P.and TAO,T.(2002).Relative efficiencies of kernel and local likelihood density estimators.J.R.Stat.Soc.Ser.B Stat. sion).Comput.Statist.7 225-281. Me1 hodol.64537-547. 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Relative efficiencies of kernel and local likelihood density estimators. J. R. Stat. Soc. Ser. B Stat. Methodol. 64 537–547. HJORT, N. L. and JONES, M. C. (1996). Locally parametric nonparametric density estimation. Ann. Statist. 24 1619–1647. JONES, M. C., MARRON, J. S. and SHEATHER, S. J. (1996). A brief survey of bandwidth selection for density estimation. J. Amer. Statist. Assoc. 91 401–407. KIM, K.-D. and HEO, J.-H. (2002). Comparative study of flood quantiles estimation by nonparametric models. J. Hydrology 260 176–193. LOADER, C. R. (1996). Local likelihood density estimation. Ann. Statist. 24 1602–1618. LOADER, C. R. (1999). Local Regression and Likelihood. Springer, New York. MARRON, J. S. and CHUNG, S. S. (2001). Presentation of smoothers: The family approach. Comput. Statist. 16 195–207. PAULSEN, O. and HEGGELUND, P. (1996). Quantal properties of spontaneous EPSCs in neurones of the Guinea-pig dorsal lateral geniculate nucleus. J. Physiology 496 759–772. RUDEMO, M. (1982). Empirical choice of histograms and kernel density estimators. Scand. J. Statist. 9 65–78. SAMIUDDIN, M. and EL-SAYYAD, G. M. (1990). On nonparametric kernel density estimates. Biometrika 77 865–874. SCOTT, D. W. (1979). On optimal and data-based histograms. Biometrika 66 605–610. SCOTT, D. W. (1992). Multivariate Density Estimation: Theory, Practice and Visualization. Wiley, New York. SCOTT, D. W. and TERRELL, G. R. (1987). Biased and unbiased cross-validation in density estimation. J. Amer. Statist. Assoc. 82 1131–1146. SEGAL, M. R. and WIEMELS, J. L. (2002). Clustering of translocation breakpoints. J. Amer. Statist. Assoc. 97 66–76. SHEATHER, S. J. (1992). The performance of six popular bandwidth selection methods on some real data sets (with discussion). Comput. Statist. 7 225–281. 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. SILVERMAN, B. W. (1981). Using kernel density estimates to investigate multimodality. J. Roy. Statist. Soc. Ser. B 43 97–99. SILVERMAN, B. W. (1986). Density Estimation for Statistics and Data Analysis. Chapman and Hall, London. SIMONOFF, J. S. (1996). Smoothing Methods in Statistics. Springer, New York. STONE, C. J. (1984). An asymptotically optimal window selection rule for kernel density estimates. Ann. Statist. 12 1285–1297. TERRELL, G. R. (1990). The maximal smoothing principle in density estimation. J. Amer. Statist. Assoc. 85 470–477. TERRELL, G. R. and SCOTT, D. W. (1985). Oversmoothed nonparametric density estimates. J. Amer. Statist. Assoc. 80 209– 214. TORTOSA-AUSINA, E. (2002). Financial costs, operating costs, and specialization of Spanish banking firms as distribution dynamics. Applied Economics 34 2165–2176. VENABLES, W. N. and RIPLEY, B. D. (2002). Modern Applied Statistics with S, 4th ed. Springer, New York. WAND, M. P. and JONES, M. C. (1995). Kernel Smoothing. Chapman and Hall, London. WOODROOFE, M. (1970). On choosing a delta-sequence. Ann. Math. Statist. 41 1665–1671