For the application of many statistical methods it is necessary to establish the measure of di erence to be used This measure has to be de ned in accordance with the nature of the data In this study we propose a measure of di erence when the data set is compositional We analyze its properties and we present examples to illustrate its performance INTRODUCTION It is well known that the usual diss...

A family of scaling corrections aimed to improve the chi-square approximation of goodness-oft test statistics in small samples, large models, and nonnormal data was proposed in Satorra and Bentler (1994). For structural equations models, Satorra-Bentler's (SB) scaling corrections are available in standard computer software. Often, however, the interest is not on the overall t of a model, but on...

The concept of weighted f Gini mean di¤ erence for convex and symmetric functions in linear spaces is introduced. Some fundamental inequalities and applications for norms are also provided. 1. Introduction The Gini mean di¤erence of the sample a = (a1; : : : ; an) 2 R is de…ned by G (a) = 1 2n2 n X

We propose a generalization of the Hukuhara di¤erence. First, the case of compact convex sets is examined; then, the results are applied to generalize the Hukuhara di¤erence of fuzzy numbers, using their compact and convex level-cuts. Finally, a similar approach is suggested to attempt a generalization of division for real intervals.

We show that the intersection of the class of 2-REA degrees with that of the !-r.e. degrees consists precisely of the class of d.r.e. degrees. We also include some applications and show that there is no natural generalization of this result to higher levels of the REA hierarchy.

Let k be a diierence eld with automorphism. Let b be an element of k, and L be a linear ordinary diierence operator with coeecients in k. A classical problem in the theory of diierence equations is to compute all the solutions in k of the equation L(y) = b. If C denotes a constant eld and if k = C(n) and n = n + 1 or n = qn, there are known algorithms (see 2] for example). Manuel Bronstein pres...

A family of scaling corrections aimed to improve the chi-square approximation of goodness-oft test statistics in small samples, large models, and nonnormal data was proposed in Satorra and Bentler (1994). For structural equations models, Satorra-Bentler's (SB) scaling corrections are available in standard computer software. Often, however, the interest is not on the overall t of a model, but on...

A family of scaling corrections aimed to improve the chi-square approximation of goodness-oft test statistics in small samples, large models, and nonnormal data was proposed in Satorra and Bentler (1994). For structural equations models, Satorra-Bentler's (SB) scaling corrections are available in standard computer software. Often, however, the interest is not on the overall t of a model, but on...

The equivalent, second equivalent and (simply) modi®ed equations for the implicit midpoint rule are shown to be asymptotically equivalent in the sense that an asymptotic analysis of these equations with the time step size as small parameter yields exactly the same results; for linear problems with constant coecients, they are also equivalent to the original ®nite di€erence scheme. Straightforw...

This report describes a series of results using the exponentiated gradient descent (EG) method recently proposed by Kivinen and Warmuth. Prior work is extended by comparing speed of learning on a nonstationary problem and on an extension to backpropagation networks. Most signi cantly, we present an extension of the EG method to temporal-di erence and reinforcement learning. This extension is co...