Kim, W. C.; Park, B. U.; Marron, J. S. Asymptotically best bandwidth selectors in kernel density estimation. (English) Zbl 0787.62043 Stat. Probab. Lett. 19, No. 2, 119-127 (1994). Summary: This paper gives asymptotically best data based choices of the bandwidth of the kernel density estimator. These bandwidth selectors attain the fastest possible rate of convergence to the desired theoretical optimum and the best possible constant coefficient in the spirit of the usual Fisher information, with the use of only nonnegative kernel estimators at all stages of the selection process. Cited in 5 Documents MSC: 62G07 Density estimation 62G20 Asymptotic properties of nonparametric inference Keywords:bandwidth selection; bandwidth factorization; best constant; asymptotically best data based choices of the bandwidth; kernel density estimator; fastest possible rate of convergence; Fisher information; nonnegative kernel estimators PDFBibTeX XMLCite \textit{W. C. Kim} et al., Stat. Probab. Lett. 19, No. 2, 119--127 (1994; Zbl 0787.62043) Full Text: DOI References: [1] Chiu, S. T., Bandwidth selection for kernel density estimation, Ann. Statist., 19, 1883-1905 (1991) · Zbl 0749.62022 [2] Fan, J.; Marron, J. S., Best possible constant for bandwidth selection, Ann. Statist., 20, 2057-2070 (1992) · Zbl 0765.62041 [3] Hall, P.; Sheather, S. J.; Jones, M. C.; Marron, J. S., On optimal data-based bandwidth selection in kernel density estimation, Biometrika, 78, 263-269 (1991) · Zbl 0733.62045 [4] Hall, P.; Marron, J. S., Lower bounds for bandwidth selection in density estimation, Probab. Theory Rel. Fields, 90, 149-173 (1991) · Zbl 0742.62041 [5] Hall, P.; Marron, J. S.; Park, B. U., Smoothed cross-validation, Probab. Theory Rel. Fields, 92, 1-20 (1992) · Zbl 0742.62042 [6] Jones, M. C.; Marron, J. S.; Park, B. U., A simple root \(n\) bandwidth selector, Ann. Statist., 19, 1919-1932 (1991) · Zbl 0745.62033 [7] Jones, M.C., J.S. Marron and S.J. Sheather (1992), Progress in data-based bandwidth selection for kernel density estimation, unpublished manuscript.; Jones, M.C., J.S. Marron and S.J. Sheather (1992), Progress in data-based bandwidth selection for kernel density estimation, unpublished manuscript. · Zbl 0897.62037 [8] Marron, J.S. (1992), Graphical understanding of higher order kernels, unpublished manuscript.; Marron, J.S. (1992), Graphical understanding of higher order kernels, unpublished manuscript. [9] Marron, J. S.; Wand, M. P., Exact mean integrated squared error, Ann. Statist., 20, 712-736 (1992) · Zbl 0746.62040 [10] Park, B. U.; Marron, J. S., Comparison of data-driven bandwidth selectors, J. Amer. Statist. Assoc., 85, 66-72 (1990) [11] Park, B. U.; Marron, J. S., On the use of pilot estimators in bandwidth selection, Nonparametric Statist., 1, 231-240 (1992) · Zbl 1263.62059 [12] Sheather, S. J.; Jones, M. C., A reliable data-based bandwidth selection method for kernel density estimation, J. Roy. Statist. Soc. Ser. B, 53, 683-690 (1991) · Zbl 0800.62219 [13] Silverman, B. W., Density Estimation for Statistics and Data Analysis (1986), Chapman and Hall: Chapman and Hall London · Zbl 0617.62042 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.