Vladimir Dragović
Bridging Statistics with Geometry and Mechanics
We emphasize the importance of bridges between statistics, mechanics, and geometry. We develop and employ links between pencils of quadrics, moments of inertia, and linear and orthogonal regressions. For a given system of points in $R^k$ representing a sample of a 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 a joint work with Borislav Gajić.
