The weighted orthogonal Procrustes problem an important class of data matching problems in multivariate data analysis is reconsidered in this paper It is shown that a steepest descent ow on the manifold of orthogonal matrices can naturally be formulated This formulation has two important implications that the constrained regression problem can be solved as an initial value problem by any availa...

this work focuses on the correction of both the coecient and the right hand side matrices of the inconsistent matrix equations $ax = b$ and $xc = d$ with orthogonal constraint. by optimal correction approach, a general representation of the orthogonal solution is obtained. this method is tested on two examples to show that the optimal correction is eective and highly accurate.

In classical multiple linear regression analysis problems will occur if the regressors are either multicollinear or if the number of regressors is larger than the number of observations. In this note a new method is introduced which constructs orthogonal predictor variables in a way to have a maximal correlation with the dependent variable. The predictor variables are linear combinations of the...

The objective of many animal experiments is to detect meaningful relationships among treatments and associated responses. Types of comparisons of means include pairwise multiple comparisons, planned orthogonal or nonorthogonal contrasts, and orthogonal polynomials. Some procedures are appropriate only for specific types of treatment designs and specific types of objectives. Pairwise, multiple c...

Classical least squares regression consists of minimizing the sum of the squared residuals. Many authors have produced more robust versions of this estimator by replacing the square by something else, such as the absolute value. In this article a different approach is introduced in which the sum is replaced by the median of the squared residuals. The resulting estimator can resist the effect of...

The relevance vector machine (RVM) is a Bayesian framework for learning sparse regression models and classifiers. Despite of its popularity and practical success, no thorough analysis of its functionality exists. In this paper we consider the RVM in the case of regression models and present two kinds of analysis results: we derive a full characterization of the behavior of the RVM analytically ...

In this paper we develop a discrete Hierarchical Basis (HB) to efficiently solve the Radial Basis Function (RBF) interpolation problem with variable polynomial order. The HB forms an orthogonal set and is adapted to the kernel seed function and the placement of the interpolation nodes. Moreover, this basis is orthogonal to a set of polynomials up to a given order defined on the interpolating no...