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+ K_{2\mathbf{G}}) (\mathbf{X}_i - \mathbf{X}_j)</math>
Thus <math>\hat{\mathbf{H}}_{\operatorname{SCV}} = \operatorname{argmin}_{\mathbf{H} \in F} \, \operatorname{SCV} (\mathbf{H})</math> is the SCV selector.<ref name="DH2005">{{Cite journal| doi=10.1111/j.1467-9469.2005.00445.x | author1=Duong, T. | author2=Hazelton, M.L. | title=Cross validation bandwidth matrices for multivariate kernel density estimation | journal=Scandinavian Journal of Statistics | year=2005 | volume=32 | issue=3 | pages=485–506}}</ref><ref>{{Cite journal| doi=10.1007/BF01205233 | author1=Hall, P. | author2=Marron, J. | author3=Park, B. | title=Smoothed cross-validation | journal=Probability Theory and Related Fields | year=1992 | volume=92 | pages=1–20| doi-access=free }}</ref>
These references also contain algorithms on optimal estimation of the pilot bandwidth matrix <strong>G</strong> and establish that <math>\hat{\mathbf{H}}_{\operatorname{SCV}}</math> converges in probability to '''H'''<sub>AMISE</sub>.
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