Friday, February 17 at 11:00am to 12:00pm
Sciences Building (SCI), 1.210
800 W. Campbell Road, Richardson, Texas 75080-3021
Title: Bridging Statistics with Geometry and Mechanics
Abstract: We emphasize the importance of connections between statistics, mechanics, and geometry. We develop and employ links between pencils of quadrics, moments of inertia, and linear and orthogonal regression. For a given system of points in R^k representing a sample of full rank, we construct a pencil of confocal quadrics which appears to be a useful geometric tool to study the data. Some of the obtained results can be seen as generalizations of classical results of Pearson on orthogonal regression. Applications include statistics of errors-in-variables models (EIV) and restricted regressions, both ordinary and orthogonal ones. For the latter, a new formula for test statistic is derived. The developed methods and results are illustrated in natural statistics examples. The talk is based on joint work with Borislav Gajić.
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