Karhunen-loève basis in goodness-of-fit tests decomposition: an evaluation

In a previous paper (Grané and Fortiana 2006) we studied a flexible class of goodness-of-fit tests associated with an orthogonal sequence, the Karhunen-Loève decomposition of a stochastic process derived from the null hypothesis. Generally speaking, these tests outperform Kolmogorov-Smirnov and Cramér-von Mises, but we registered several exceptions. In this work we investigate the cause of these anomalies and, more precisely, whether and when such poor behaviour may be attributed to the orthogonal sequence itself, by replacing it with the Legendre polynomials, a commonly used basis for smooth tests. We find an easily computable formula for the Bahadur asymptotic relative efficiency, a helpful quantity in choosing an adequate basis

A scale-free adaptive statistic for testing exponentiality against Weibull and generalized Pareto distributions

In Fortiana and Grané (2002) we study a scale-free statistic, based on Hoeffding's maximum correlation, for testing exponentiality. This statistic admits an expansion along a countable set of orthogonal axes, originating a sequence of statistics. Linear combinations of a given number p of terms in this sequence can be written as a quotient of L-statistics. In this paper we propose a scalefree adaptive statistic for testing exponentiality with optimal power against a specific alternative. We obtain its exact distribution and compare it with other scale-free statistics for testing exponentiality, such as the Stephens' modification of the Shapiro-Wilk statistic, the Gini statistic and the Qn statistic defined in Fortiana and Grané (2002)

Implementing PLS for distance-based regression: computational issues

Distance-based regression allows for a neat implementation of the Partial Least Squares recurrence. In this paper we address practical issues arising when dealing with moderately large datasets (n ~ 10^4) such as those typical of automobile insurance premium calculations

On the surjectivity of the Ribenboim representation of a lattice ordered group.

Sobreyectividad ; Grupo ordenado ; Representación de grupos ; Retículo

Propiedades topológicas de los grupos de isometría de un grupo reticulado.

This paper deals with the topological properties of groups of isometries of lattice-ordered groups and f-rings. The topologies considered are order-topology and the topology defined by null-sequences

On isometries of lattice ordered groups and rings.

This paper has a main objective: the study, classification and characterization of isometries of a lattice ordered group. The concept of group of isometries M(G) of a lattice ordered group G is introduced, as well as those of group of homogeneous symmetries H(G) and translations T(G). First the elementary case of totally ordered groups is studied, and then, by using the representation of groups (and f-rings) in a product of totally ordered ones, the concept of admisible set of indexes associated to a symmetry is introduced.El contenido de este trabajo tiene un objetivo fundamental: el estudio, clasificación y caracterización de las isometrías de un grupo reticulado. Se introducen los conceptos de grupo de isometrías M(G) de un grupo reticulado G, grupo de simetrías homogéneas H(G) y traslaciones T(G). Se estudia primero el caso elemental de los grupos totalmente ordenados y utilizando luego las representaciones de los grupos (y f-anillos) en un producto de totalmente ordenados, se introduce el concepto de conjunto admisible de índices asociado a una simetría

Invariant sets in the group of isometries of a lattice-ordered group.

This paper deals with the invariant sets in the group of isometries of a lattice-ordered group. It is shown that all the invariant sets are union of some transitivity subsets of the spheres