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<math> \left\| \mathbf{X_1-X_0W} \right\|_V = \sqrt{(X_1-X_0W)'V(X_1-X_0W)}</math>, where ''''V'''' is defined as (k×k) symmetric and positive semidefinite matrix. V* is chosen among all positive definite and diagnal matrices such that the mean square prediction error(MSPE) of the outcome variable is minimized over pre-intervention period.
<ref>\Synthetic Control Methods for Comparative Case Studies: Estimating the Effect of California's Tobacco Control Program."</ref>
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