= Least-squares cross-validation for density bandwidth
{title2=$\operatorname{CV}(h)=R(\widehat f_h)-\frac2n\sum_i\widehat f_{h,-i}(X_i)$}
= Least-squares density cross-validation
{synonym}
Minimize the displayed criterion using a <Leave-one-out cross-validation> estimate in the second term. Its expectation is the exact <mean integrated squared error> minus $R(f)$, which does not depend on h. With standard smoothness and appropriate search ranges, the chosen bandwidth is asymptotically optimal. Its relative fluctuations are ordinarily of order $n^{-1/10}$, considerably larger than the estimation error achievable by well-chosen plug-in pilots.
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