## Statistics Colloquium: Dr. Derek Young

#### University of Kentucky

**Title: **Hyperrectangular Tolerance and Prediction Regions for Setting Multivariate

**Abstract: **Reference regions are widely used in clinical chemistry and laboratory medicine to interpret the results of biochemical or physiological tests of patients. There are well-established methods in the literature for reference limits for univariate measurements, however, only limited methods are available for the construction of multivariate reference regions. This is because traditional multivariate statistical regions (e.g., confidence, prediction, and tolerance regions) are not constructed based on a hyperrectangular geometry. We address this problem by developing multivariate hyperrectangular nonparametric tolerance regions for setting the reference regions. Our approach utilizes statistical data depth to determine which points to trim and then the extremes of the trimmed dataset are used as the faces of the hyperrectangular region. We also specify the number of points to trim based on previously-established asymptotic results. Extensive coverage results show the favorable performance of our algorithm provided a minimum sample size criterion is met. Our procedure is used to obtain reference regions for addressing two important clinical problems: (1) characterizing insulin-like growth factor concentrations in the serum of adults and (2) assessing kidney function in adolescents. This is a joint work with Thomas Mathew (UMBC).