= Generalized cross-validation
{title2=$\mathrm{GCV}=\dfrac{\|Y-SY\|^2/n}{(1-\operatorname{tr}(S)/n)^2}$}
= GCV
{c}
{synonym}
For a fixed <linear smoother>, generalized cross-validation replaces the individual leverage corrections of <Leave-one-out cross-validation> by their average. It selects smoothing parameters by minimizing the displayed criterion. It approximates a predictive error criterion; it is not a universal exact estimate of future error and requires care when observation errors are dependent.
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