Donald E. Ramirez

Weakly almost periodic functionals on the Fourier algebra

The theory of weakly almost periodic functionals on the Fourier algebra is herein developed. It is the extension of the theory of weakly almost periodic functions on locally compact abelian groups to the duals of compact groups. The complete direct product of a countable collection of nontrivial compact groups furnishes an important example for some of the constructions.

Krawtchouk Polynomials and the Symmetrization of Hypergroups

This paper introduces the method of symmetrization of the measure algebra of a compact

Computing hyperelliptic integrals for surface measure of ellipsoids

P_ *

An Expert Model Selection Approach to Determine the “Best” Pattern Structure in Factor Analysis Models

-hypergroup. This method is used to form a measure algebra whose characters are Krawtchouk polynomials (these are the finite sets of polynomials orthogonal with respect to the binomial distribution on

Misspecified T2 tests. II. series expansions

\{ 0,1, \cdots ,N\}

Efficiency comparisons in linear inference

. As a further application, one derives a theorem about nonnegative expansions of one family of Krawtchouk polynomials in terms of another family.

Bounded projections on Fourier-Stieltjes transforms

An algorithm for computing a class of hyperelliptic integrals and for determining the surface measure of ellipsoids is described. The algorithm is used to construct an omnibus optimal-design criterion.

An adjusted likelihood-ratio approach to the behrens-fisher problem

This paper introduces and develops an expert data-analytic model selection approach based on Akaike’s Information Criterion (AIC) and asymptotically Consistent Akaike’s Information Criterion (CAIC), to choose the number of factors, m, and to determine the “best” factor pattern structure among all possible patterns under the orthogonal factor model using Mallows’ Cp Criterion.

Uniform approximation by Fourier–Stieltjes coefficients

Properties of nonstandard Hotellings (1931) T2 distributions are studied under models having misspecified scale. Local and global bounds on truncation errors are given for a weighted series of F-distributions, extending the work of Kotz et al. (1967) to include nonstandard T2 distributions

Revision: Variance Inflation in Regression

Abstract A new approach to comparative design efficiency is given in linear estimation and in tests for linear hypotheses. In contrast to others, this approach gives a complete assessment of two designs for any model on identifying precisely the subspaces of parameters for which one design is more efficient than another, or two designs are equally efficient. Local and global bounds on relative design efficiencies are given with reference to these subspaces, and connections to information functionals are noted. The relative influences of design points with regard to deletion and augmentation are examined and related to measures of influence from the literature. Our approach provides numerical diagnostics for use in design evaluation before an experiment has been run. The concepts are illustrated with reference to selected second-order designs.