Chacón, J. E.; Tenreiro, C. Data-based choice of the number of pilot stages for plug-in bandwidth selection. (English) Zbl 1319.62074 Commun. Stat., Theory Methods 42, No. 12, 2200-2214 (2013). Summary: The choice of the bandwidth is a crucial issue for kernel density estimation. Among all the data-dependent methods for choosing the bandwidth, the direct plug-in method has shown a particularly good performance in practice. This procedure is based on estimating an asymptotic approximation of the optimal bandwidth, using two “pilot” kernel estimation stages. Although two pilot stages seem to be enough for most densities, for a long time the problem of how to choose an appropriate number of stages has remained open. Here we propose an automatic (i.e., data-based) method for choosing the number of stages to be employed in the plug-in bandwidth selector. Asymptotic properties of the method are presented and an extensive simulation study is carried out to compare its small-sample performance with that of the most recommended bandwidth selectors in the literature. Cited in 1 Document MSC: 62G05 Nonparametric estimation 62G07 Density estimation 62G20 Asymptotic properties of nonparametric inference Keywords:bandwidth selection; density estimation; kernel method; plug-in rule PDF BibTeX XML Cite \textit{J. E. Chacón} and \textit{C. Tenreiro}, Commun. Stat., Theory Methods 42, No. 12, 2200--2214 (2013; Zbl 1319.62074) Full Text: DOI References: [1] Aldershof , B. ( 1991 ). Estimation of integrated squared density derivatives. Ph.D. thesis, University of North Carolina, Chapel Hill, NC . [2] DOI: 10.1093/biomet/71.2.353 · doi:10.1093/biomet/71.2.353 [3] DOI: 10.1016/0167-9473(92)00066-Z · Zbl 0937.62518 · doi:10.1016/0167-9473(92)00066-Z [4] Chacón J. E., Statist. Sinica 17 pp 289– (2007) [5] Hall P., Ann. Statist. 11 pp 1156– (1983) · Zbl 0599.62051 · doi:10.1214/aos/1176346329 [6] DOI: 10.1016/0167-7152(87)90083-6 · Zbl 0628.62029 · doi:10.1016/0167-7152(87)90083-6 [7] DOI: 10.1007/BF00363516 · Zbl 0588.62052 · doi:10.1007/BF00363516 [8] DOI: 10.1214/aos/1176350697 · Zbl 0637.62035 · doi:10.1214/aos/1176350697 [9] DOI: 10.1016/0167-7152(91)90116-9 · Zbl 0724.62040 · doi:10.1016/0167-7152(91)90116-9 [10] Jones M. C., Comput. Statist. 11 pp 337– (1996) [11] DOI: 10.1016/0167-7152(91)90116-9 · Zbl 0724.62040 · doi:10.1016/0167-7152(91)90116-9 [12] DOI: 10.1080/10485250903194003 · Zbl 1264.62029 · doi:10.1080/10485250903194003 [13] DOI: 10.1214/aos/1176348653 · Zbl 0746.62040 · doi:10.1214/aos/1176348653 [14] DOI: 10.1080/01621459.1990.10475307 · doi:10.1080/01621459.1990.10475307 [15] DOI: 10.1080/10485259208832524 · Zbl 1263.62059 · doi:10.1080/10485259208832524 [16] Rudemo M., Scand. J. Statist. 9 pp 65– (1982) [17] Sheather S. J., J. Roy. Statist. Soc. Ser. B Statist. Methodol. 53 pp 683– (1991) [18] Silverman B. W., Density Estimation for Statstics and Data Analysis (1986) · doi:10.1007/978-1-4899-3324-9 [19] DOI: 10.1007/978-1-4612-4026-6 · doi:10.1007/978-1-4612-4026-6 [20] DOI: 10.1214/aos/1176346792 · Zbl 0599.62052 · doi:10.1214/aos/1176346792 [21] DOI: 10.1016/S0167-7152(03)00176-7 · Zbl 1113.62317 · doi:10.1016/S0167-7152(03)00176-7 [22] DOI: 10.1080/01621459.1990.10476223 · doi:10.1080/01621459.1990.10476223 [23] Wand M. P., Kernel Smoothing (1995) · Zbl 0854.62043 · doi:10.1007/978-1-4899-4493-1 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.