B1409
Title: An adaptive weighted mean for multivariate location estimation
Authors: Keith Knight - University of Toronto (Canada) [presenting]
Abstract: Given multivariate observations $x_1 , \cdots , x_n$ from some distribution, location estimates are considered that are weighted means: $\hat{\mu} = w_1 x_1 + \cdots + w_n x_n$ where the weights $\{ w_i \}$ are non-negative and sum to 1. The proposed method selects the weights so that the points $\{ w_i^{1/2} ( x_i - \hat{\mu} ) \}$ lie within an ellipsoid where the points with small weights lie closer to the boundary of the ellipsoid; $\hat{\mu}$ is affine equivariant and might be viewed as a multivariate Winsorized mean. The weights $\{ w_i \}$ can be computed using an iterative algorithm that computes a QR decomposition at each step. The method also has a dimension reduction feature: if a sufficient number of observations lie in or close to a lower dimensional subspace, these observations will receive the highest weights.
