Orthogonalization of vectors with minimal adjustment

Two transformations are proposed that give orthogonal components with a one-to-one correspondence between the original vectors and the components. The aim is that each component should be close to the vector with which it is paired, orthogonality imposing a constraint. The transformations lead to a variety of new statistical methods, including a unified approach to the identification and diagnosis of collinearities, a method of setting prior weights for Bayesian model averaging, and a means of calculating an upper bound for a multivariate Chebychev inequality. One transformation has the property that duplicating a vector has no effect on the orthogonal components that correspond to nonduplicated vectors, and is determined using a new algorithm that also provides the decomposition of a positive-definite matrix in terms of a diagonal matrix and a correlation matrix. The algorithm is shown to converge to a global optimum

Geometry of Goodness-of-Fit Testing in High Dimensional Low Sample Size Modelling

We introduce a new approach to goodness-of-fit testing in the high dimensional, sparse extended multinomial context. The paper takes a computational information geometric approach, extending classical higher order asymptotic theory. We show why the Wald – equivalently, the Pearson X2 and score statistics – are unworkable in this context, but that the deviance has a simple, accurate and tractable sampling distribution even for moderate sample sizes. Issues of uniformity of asymptotic approximations across model space are discussed. A variety of important applications and extensions are noted

Computational information geometry in statistics: foundations

This paper lays the foundations for a new framework for numerically and computationally applying information geometric methods to statistical modelling

Local mixtures of the exponential distribution

Mixture model, Local mixtures, Laplace expansion, Scale dispersion models, Affine geometry,

La calidad del servicio de préstamo interbibliotecario en la Red de Bibliotecas del CSIC: cinco años progresando (1992-1996)

En ésta comunicación se analiza el préstamo interbibliotecario de la Red de Bibliotecas del CSIC desde el año 1992 al año 1996 evaluando el progreso del servicio a través de tablas comparativas

Towards the Geometry of Model Sensitivity: An Illustration

In statistical practice model building, sensitivity and uncertainty are major concerns of the analyst. This paper looks at these issues from an information geometric point of view. Here, we define sensitivity to mean understanding how inference about a problem of interest changes with perturbations of the model. In particular it is an example of what we call computational information geometry. The embedding of simple models in much larger information geometric spaces is shown to illuminate these critically important issues