Universal Inadmissibility of Least Squares Estimator

Computing the Least Median of Squares Estimator

In modern statistics, the robust estimation of parameters of a regression hyperplane is a central problem, i. e., an estimation that is not or only slightly affected by outliers in the data. In this paper we will consider the least median of squares (LMS) estimator. For n points in d dimensions we describe a randomized algorithm for LMS running in O ( nd ) time and O(n) space, for d fixed, and ...

Universal Linear Least - Squares Prediction

An approach to the problem of linear prediction is discussed that is based on recent developments in the universal coding and computational learning theory literature. This development provides a novel perspective on the adaptive filtering problem, and represents a significant departure from traditional adaptive filtering methodologies. In this context, we demonstrate a sequential algorithm for...

The Multivariate Least Trimmed Squares Estimator

In this paper we introduce the least trimmed squares estimator for multivariate regression. We give three equivalent formulations of the estimator and obtain its breakdown point. A fast algorithm for its computation is proposed. We prove Fisherconsistency at the multivariate regression model with elliptically symmetric error distribution and derive the influence function. Simulations investigat...

Coarse-to-Fine Least Squares Motion Estimator

An optimality property of the integer least-squares estimator

A probabilistic justi®cation is given for using the integer least-squares (LS) estimator. The class of admissible integer estimators is introduced and classical adjustment theory is extended by proving that the integer LS estimator is best in the sense of maximizing the probability of correct integer estimation. For global positioning system ambiguity resolution, this implies that the success r...