References
- Parzen E. On estimation of a probability density function and mode. Ann Math Statist. 1962;33:1065–1076. doi: 10.1214/aoms/1177704472
- Rosenblatt M. Remarks on some non-parametric estimates of a density function. Ann Math Statist. 1956;27:832–837. doi: 10.1214/aoms/1177728190
- Bosq D, Lecoutre J-P. Théorie de l'estimation fonctionnelle. Paris: Economica; 1987.
- Devroye L, Györfi L. Nonparametric density estimation: the L view. New York: Wiley; 1985.
- Silverman BW. Density estimation for statistics and data analysis. London: Chapman and Hall; 1986.
- Simonoff JS. Smoothing methods in statistics. New York: Springer; 1996.
- Tsybakov AB. Introduction to nonparametric estimation. London: Springer; 2009.
- Wand MP, Jones MC. Kernel smoothing. New York: Chapman & Hall; 1995.
- Tenreiro C. A weighted least-squares cross-validation bandwidth selector for kernel density estimation. Comm Statist Theory Methods. 2017;46:3438–3458. doi: 10.1080/03610926.2015.1062108
- Woodroofe M. On choosing a delta-sequence. Ann Math Statist. 1970;41:1665–1671. doi: 10.1214/aoms/1177696810
- Nadaraya EA. On the integral mean square error of some nonparametric estimates for the density function. Theory Probab Appl. 1974;19:133–141. doi: 10.1137/1119010
- Deheuvels P, Hominal P. Estimation automatique de la densité. Rev Statist Appl. 1980;28:25–55.
- Chacón JE, Montanero J, Nogales AG, et al. On the existence and limit behaviour of the optimal bandwidth for kernel density estimation. Statist Sinica. 2007;17:289–300.
- Hall P, Marron JS. Extent to which least-squares cross-validation minimizes integrated square error in nonparametric density estimation. Probab Theory Related Fields. 1987;74:567–581. doi: 10.1007/BF00363516
- Hall P, Marron JS. Lower bounds for bandwidth selection in density estimation. Probab Theory Related Fields. 1991;90:149–173. doi: 10.1007/BF01192160
- Tenreiro C. Fourier series based direct plug-in bandwidth selectors for kernel density estimation. J Nonparametr Stat. 2011;23:533–545. doi: 10.1080/10485252.2010.537337
- Chacón JE, Tenreiro C. Exact and asymptotically optimal bandwidths for kernel estimation of density functionals. Methodol Comput Appl Probab. 2012;14:523–548. doi: 10.1007/s11009-011-9243-x
- Jones MC, Sheather SJ. Using non-stochastic terms to advantage in kernel-based estimation of integrated squared density derivatives. Statist Probab Lett. 1991;11:511–514. doi: 10.1016/0167-7152(91)90116-9
- Chacón JE, Tenreiro C. Data-based choice of the number of pilot stages for plug-in bandwidth selection. Comm Statist Theory Methods. 2013;42:2200–2214. doi: 10.1080/03610926.2011.606486
- Wand MP. KernSmooth: functions for kernel smoothing supporting Wand & Jones (1995). R package version 2.23-16. 2019. Available from: http://CRAN.R-project.org/package=KernSmooth.
- Laurent B. Estimation of integral functionals of a density and its derivatives. Bernoulli. 1997;3:181–211. doi: 10.2307/3318586
- R Development Core Team. R: a language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing; 2019. Available from: http://www.R-project.org.
- Greblicki W, Pawlak M. Hermite series estimates of a probability density and its derivatives. J Multivariate Anal. 1984;15:174–182. doi: 10.1016/0047-259X(84)90024-1
- Bickel PJ, Ritov Y. Estimating integrated squared density derivatives: sharp best order of convergence estimates. Sankhya Ser A. 1988;50:381–393.
- Fan J, Marron JS. Best possible constant for bandwidth selection. Ann Statist. 1992;20:2057–2070. doi: 10.1214/aos/1176348902
- Marron JS, Wand MP. Exact mean integrated squared error. Ann Statist. 1992;20:712–736. doi: 10.1214/aos/1176348653
- Rudemo M. Empirical choice of histograms and kernel density estimators. Scand J Statist. 1982;9:65–78.
- Bowman AW. An alternative method of cross-validation for the smoothing of density estimates. Biometrika. 1984;71:353–360. doi: 10.1093/biomet/71.2.353
- Schwartz SC. Estimation of probability density by an orthogonal series. Ann Math Statist. 1967;38:1261–1265. doi: 10.1214/aoms/1177698795
- Hart JD. On the choice of a truncation point in Fourier series density estimation. J Stat Comput Simul. 1985;21:95–116. doi: 10.1080/00949658508810808
- Walter G. Properties of Hermite series estimation of probability density. Ann Statist. 1977;5:1258–1264. doi: 10.1214/aos/1176344013
- Lee AJ. U-statistics, theory and practice. New York: Marcel Dekker; 1990.
- Greblicki W, Pawlak M. Pointwise consistency of the Hermite series density estimate. Statist Probab Lett. 1985;3:65–69. doi: 10.1016/0167-7152(85)90026-4
- Hall P, Sheather SJ, Jones MC, et al. On optimal data-based bandwidth selection in kernel density estimation. Biometrika. 1991;78:263–269. doi: 10.1093/biomet/78.2.263