Luca Bagnato

The Autodependogram: A Graphical Device to Investigate Serial Dependences

In this article the serial dependences between the observed time series and the lagged series, taken into account one-by-one, are graphically analysed by what we have chosen to call the ‘autodependogram’. This tool is a sort of natural nonlinear counterpart of the well-known autocorrelogram used in the linear context. The autodependogram is based on the simple idea of using, instead of autocorrelations at varying time lags, the χ2-test statistics applied to convenient contingency tables. The efficacy of this graphical device is confirmed by real and artificial time series and by simulations from certain classes of well-known models, characterized by randomness and by different kinds of linear and nonlinear dependences.

On the Spectral Decomposition in Normal Discriminant Analysis

This article enlarges the covariance configurations, on which the classical linear discriminant analysis is based, by considering the four models arising from the spectral decomposition when eigenvalues and/or eigenvectors matrices are allowed to vary or not between groups. As in the classical approach, the assessment of these configurations is accomplished via a test on the training set. The discrimination rule is then built upon the configuration provided by the test, considering or not the unlabeled data. Numerical experiments, on simulated and real data, have been performed to evaluate the gain of our proposal with respect to the linear discriminant analysis.

Radium isotopes in Estonian groundwater: measurements, analytical correlations, population dose and a proposal for a monitoring strategy.

In some areas of Estonia, groundwater contains a significant number of natural radionuclides, especially radium isotopes, which may cause radiation protection concern depending on the geological structure of the aquifer. Indeed, the parametric value of 0.1 mSv y⁻¹ for the total indicative dose established by European Directive 98/83/EC, adopted as a limit value in Estonian national legislation, is often exceeded. A Twinning Project between Estonia and Italy was carried out within the framework of the Estonian Transition Facility Programme, sponsored by the European Union. Its aims were to assess the radiological situation of Estonian groundwater and related health consequences. The first step was a study of Estonian aqueducts and the population served by them, and a thorough analysis of the radiological database for drinking water, from which the relevant effective doses for the population were obtained. Particular attention was devoted to doses to children and infants. Correlations between the chemical parameters were investigated, in order to suggest the best possible analytical approach. Lastly, a monitoring strategy, i.e. sampling points and sampling frequencies, was proposed.

Checking Serial Independence of Residuals from a Nonlinear Model

In this paper the serial independence tests known as SIS (Serial Independence Simultaneous) and SICS (Serial Independence Chi-Square) are considered. These tests are here contextualized in the model validation phase for nonlinear models in which the underlying assumption of serial independence is tested on the estimated residuals. Simulations are used to explore the performance of the tests, in terms of size and power, once a linear/nonlinear model is fitted on the raw data. Results underline that both tests are powerful against various types of alternatives.

Using the Autodependogram in Model Diagnostic Checking

In this chapter the autodependogram is contextualized in model diagnostic checking for nonlinear models by studying the lag-dependencies of the residuals. Simulations are considered to evaluate its effectiveness in this context. An application to the Swiss Market Index is also provided.

A Latent Variable Approach to Modelling Multivariate Geostatistical Skew-Normal Data

In this paper we propose a spatial latent factor model to deal with multivariate geostatistical skew-normal data. In this model we assume that the unobserved latent structure, responsible for the correlation among different variables as well as for the spatial autocorrelation among different sites is Gaussian, and that the observed variables are skew-normal. For this model we provide some of its properties like its spatial autocorrelation structure and its finite dimensional marginal distributions. Estimation of the unknown parameters of the model is carried out by employing a Monte Carlo Expectation Maximization algorithm, whereas prediction at unobserved sites is performed by using closed form formulas and Markov chain Monte Carlo algorithms. Simulation studies have been performed to evaluate the soundness of the proposed procedures.

Testing for serial independence: Beyond the Portmanteau approach

ABSTRACT Portmanteau tests are typically used to test serial independence even if, by construction, they are generally powerful only in presence of pairwise dependence between lagged variables. In this article, we present a simple statistic defining a new serial independence test, which is able to detect more general forms of dependence. In particular, differently from the Portmanteau tests, the resulting test is powerful also under a dependent process characterized by pairwise independence. A diagram, based on p-values from the proposed test, is introduced to investigate serial dependence. Finally, the effectiveness of the proposal is evaluated in a simulation study and with an application on financial data. Both show that the new test, used in synergy with the existing ones, helps in the identification of the true data-generating process. Supplementary materials for this article are available online.

The Kullback–Leibler autodependogram

ABSTRACT The autodependogram is a graphical device recently proposed in the literature to analyze autodependencies. It is defined computing the classical Pearson -statistics of independence at various lags in order to point out the presence lag-depedencies. This paper proposes an improvement of this diagram obtained by substituting the -statistics with an estimator of the Kullback–Leibler divergence between the bivariate density of two delayed variables and the product of their marginal distributions. A simulation study, on well-established time series models, shows that this new autodependogram is more powerful than the previous one. An application to a well-known financial time series is also shown.

The Role of Orthogonal Polynomials in Tailoring Spherical Distributions to Kurtosis Requirements

This paper carries out an investigation of the orthogonal-polynomial approach to reshaping symmetric distributions to fit in with data requirements so as to cover the multivariate case. With this objective in mind, reference is made to the class of spherical distributions, given that they provide a natural multivariate generalization of univariate even densities. After showing how to tailor a spherical distribution via orthogonal polynomials to better comply with kurtosis requirements, we provide operational conditions for the positiveness of the resulting multivariate Gram–Charlier-like expansion, together with its kurtosis range. Finally, the approach proposed here is applied to some selected spherical distributions.

Model-Based Classification Via Patterned Covariance Analysis

This work deals with the classification problem in the case that groups are known and both labeled and unlabeled data are available. The classification rule is derived using Gaussian mixtures where covariance matrices are given according to a multiple testing procedure which asesses a pattern among heteroscedasticity, homometroscedasticity, homotroposcedasticity, and homoscedasticity. The mixture models are then fitted using all available data (labeled and unlabeled) and adopting the EM and the CEM algorithms. The performance of the proposed procedure is evaluated by a simulation study.