Rigoberto Pérez

A note on smooth approximation capabilities of fuzzy systems

Modeling and prediction in some systems requires the simultaneous approximation of mappings and their derivatives to a certain finite order. In this paper, universal approximation capabilities of fuzzy systems are extended to this situation, by showing the denseness of some general classes of fuzzy models in appropriate function spaces where distance between functions is defined in terms of their derivatives. Requirements are generally very mild, and are often limited to imposing sufficient differentiability conditions on the classes of fuzzy systems to be used. The cases covered by this paper include additive fuzzy systems with Gaussian membership functions and general additive fuzzy models with realistic membership functions. Some potential application fields are considered, including examples from economics and time series prediction.

A family of measures of uncertainty involving utilities: Definition, properties, applications and statistical inferences

Consider an experiment involving the observation of a discrete random variable, or quantitative classification process. When, in addition to the probability of each value or class we know its “utility” (or, more precisely, we can quantify the “nature” of each value or class), the “uncertainty corresponding to the utilities” may be evaluated. In this paper, we are first going to introduce a family of Measures of Uncertainty involving Utilities and several properties of this family are studied. Then, some immediate applications are discussed: the definition of criteria for Comparing Experiments in Statistical Decision problems, and the quantification of the Inequality with respect to an economical attribute or the Industrial Concentration. Finally, we will analyze the asymptotic behaviour of the measures in simple random sampling, and some related problems.

Unbiased estimation of income inequality

In a previous paper Gastwirth shows that a broad family of measures of inequality can be accurately estimated when the tax data are known in groups (more precisely, when we know the number of returns in each of several class intervals and their corresponding average income). In the present paper we show that some measures of the preceding family can be unbiasedly estimated when the tax data are individually known for a sample from the population. Specifically, we construct unbiased estimators of a particular measure of inequality in the samplings with and without replacement, and in the stratified samplings with and without replacement.

On Economic Applications of Information Theory

In many of his writings, lectures and talks Pedro Gil emphasized the wide variety of economic applications of Information Theory. In this paper, as a tribute to him, we aim to provide some insight into this topic, mainly referred to income inequality, industrial concentration and economic forecasting.