Working papers of the Federal Reserve Bank of Cleveland are preliminary materials circulated to stimulate discussion and critical comment on research in progress. They may not have been subject to the formal editorial review accorded official Federal Reserve Bank of Cleveland publications. The views stated herein are those of the authors and are not necessarily those of the Federal Reserve Bank...

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Detecting outlying observations is an important step in any analysis, even when robust estimates are used. In particular, the robustified Mahalanobis distance is a natural measure of outlyingness if one focuses on ellipsoidal distributions. However, it is well known that the asymptotic chi-square approximation for the cutoff value of the Mahalanobis distance based on several robust estimates (l...

When a struggling high school may be placed on turnaround status during bid for bond, the district considers replacing beloved principal with record of low test scores an unpopular whose shows increased student achievement. The board must decide whether to prioritize finances, community support, achievement, or state-level demands. This case presents many difficult decisions schools and distric...

Principal Component Analysis is a method for reducing the dimensionality of datasets while also limiting information loss. It accomplishes this by producing uncorrelated variables that maximize variance one after other. The accepted criterion evaluating Component’s (PC) performance λ_j/tr(S) where tr(S) denotes trace covariance matrix S. standard procedure to determine how many PCs should be ma...