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Abstract:
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Statistical data depth provides a measure of how deep a point is with respect to an underlying distribution or to a random sample. Depth values, thus, provide a center-outward ranking of multivariate data. We present two novel depth-based approaches to construct statistical regions for quite distinct applications. First, we use a depth-based ordering to construct hyperrectangular prediction regions and tolerance regions. These are then used as reference regions in the area of laboratory medicine. Second, we use tolerance regions and data depth to inform cutoff levels for Winsorizing/trimming in multivariate datasets. This approach results in Winsorized/trimmed regions that reduce the impact of influential observations when calculating finite population estimates from survey data. We end with a brief discussion of some related novel procedures currently being investigated.
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