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It has been established that the plug-in and smoothed cross validation selectors (given a single pilot bandwidth '''G''') both converge at a relative rate of ''O<sub>p</sub>''(''n''<sup>−2/(''d''+6)</sup>) <ref name="DH2005" /><ref>{{Cite journal| doi=10.1016/j.jmva.2004.04.004 | author1=Duong, T. | author2=Hazelton, M.L. | title=Convergence rates for unconstrained bandwidth matrix selectors in multivariate kernel density estimation | journal=Journal of Multivariate Analysis | year=2005 | volume=93 | issue=2 | pages=417–433| doi-access=free }}</ref> i.e., both these data-based selectors are consistent estimators.
[[File:Old Faithful Geyser KDE with plugin bandwidth.png|thumb|250px|alt=Old Faithful Geyser data kernel density estimate with plug-in bandwidth matrix.|Old Faithful Geyser data kernel density estimate with plug-in bandwidth matrix.]]
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