0000000001031856
AUTHOR
Salvatore Bologna
Una procedura sequenziale di stima di punto di cambiamento
In this paper we propose a sequential procedure for the estimation of a change-point when a change has occurred in the distribution that governs the process which generates the observations. The procedure applies whether the distribution functions involved are completely specified or they contain unknown parameters to be estimated. The procedure is based on the Kolmogorov-Smirnov test of goodness of fit, or an appropriate different test such as the chi-square test, and satisfies the optimality condition defined by the maximization of the sum of the p-values involved.
A class of multivariate extreme value distributions with heterogeneous margins
Many problems which involve applications of extreme value theory show an essential multivariate nature and recent development of the theory in this field deal with the construction of multivariate extreme value distributions. Owing to the nature of the problem under examination, extreme values to be analyzed jointly may have different limiting distributions, but it seems that explicit expressions of multivariate extreme value distributions with heterogeneous margins are not present in the literature. In this paper we consider the problem of constructing multivariate extreme value distributions with univariate marginal extreme value distributions not belonging or, more generally, not all bel…
A multivariate Gompertz-type distribution
Multivariate extensions of the Gompertz distribution are plausible models for the study of several dependent populations with a Gompertz law of growth or multivariate survival data. In this paper we introduce a multivariate distribution with univariate marginal distributions of Gompertz-type form. The new distribution is expressed in closed form and shows symmetry in the component variables. We provide explicit expressions for the first moments which are functions of the Euler constant. Specifically we develop a trivariate Gompertz-type distribution and afterwards consider the multivariate case as an immediate extension of this. The problem of estimating the parameters of the new multivaria…
A CLASS OF MULTIVARIATE TRANSFORMED-EXPONENTIAL DISTRIBUTIONS
In finance it is commonly accepted that heavy-tailed distributions are appropriate for modelling financial asset return variables and part of the financial literature has recently focused on them. Much less attention has been dedicated to the construction of joint models of asset returns unable to describe an adequate dependence structure between all these variables. In this paper we propose a procedure for constructing multivariate distributions with given heterogeneous heavy-tailed marginal distributions as a possible (under certain conditions) alternative to the copula approach. The procedure bases on the marginal transformation method and, for given plausible specifications of the margi…
A new OLS-based procedure for clusterwise linear regression
Data heterogeneity, within a (linear) regression framework, often suggests the use of a Clusterwise Linear Regression (CLR) procedure, which implies, among other things, the estimate of the appropriate number of clusters as well as the cluster membership of each unit. The approaches to the estimation of a CLR model are essentially based on the Ordinary Least Square (OLS) criterion or the likelihood criterion. In this paper, in a context of OLS approach, we propose an estimation of the model making use of an algorithm based on a threshold criterion for the determination coefficient of each cluster, to identify the appropriate number of clusters, and of a modified Spath's algorithm, to estima…
A multivariate powered half-normal distribution
The half-normal distribution has applications in various contexts, particularly in economic analysis (to describe, for example, inefficiency variables), reliability analysis and quality control. However, it seems that, still in the recent literature, interest in forms of multivariate distribution with half-normal marginals is remained at a low level. This problem arises, for example, in the context of economic analysis when it needs to examine inefficiency variables simultaneously. Furthermore, from a robustness perspective, the distributional assumption of half-normality may show itself too strong (or the model too rigorous) and to be inconsistent with the real data, thus motivating the ne…
A class of multivariate type I generalized logistic distributions
The logistic distribution has found important applications in many different fields and several different forms of generalizations have been proposed in the literature. However it seems, with a few exceptions, that there are not in the literature forms of multivariate generalized logistic distributions. In this paper we focus on the type I generalized logistic distribution and, based on a procedure of multivariate transformation of multivariate exponential distributions, we introduce a class of multivariate type I generalized logistic distributions. We provide some examples of bivariate and multivariate distributions of this class.
Second-order interaction in a Trivariate Generalized Gamma Distribution
The concept of second- (and higher-) order interaction is widely used in categorical data analysis, where it proves useful for explaining the interdependence among three (or more) variables. Its use seems to be less common for continuous multivariate distributions, most likely owing to the predominant role of the Multivariate Normal distribution, for which any interaction involving more than two variables is necessarily zero. In this paper we explore the usefulness of a second-order interaction measure for studying the interdependence among three continuous random variables, by applying it to a trivariate Generalized Gamma distribution proposed by Bologna(2000).