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COVID-19: How to estimate the percentages of asymptomatic and immune individuals
Oliveira, Manuela; Mexia, João T.; Garção, Eugénio; Grilo, Luís M.Epidemiology focuses on the identification of patterns in disease occurrence in order to provide information that may be useful to help prevent it. The research of how a disease may be transmitted is influential for that identification. In the case of COVID-19 this research should focus on the relations between the disease and the populations of susceptible individuals that might be infected. In this context, w...
A risk model for Forest fires based on asymptotic results for multivariate coll...
Cantarinha, Ana G.; Moreira, Elsa E.; Oliveira, Manuela; Marques, Susete; Mexia, João T.In this paper we propose an new approach to multivariate collective models based on asymptotic distibutions, since the modeling problems posed have large samples. Collective risk models play an important part in Risk Theory and in Actuarial Mathematics. Inference based on these models is centered on claims totals. However, the new approach has in mind a different kind of risk, the risk of forest fires, where th...
STATIS methodology: an overview
Grilo, Luís M.; Oliveira, Manuela; Garção, Eugénio; Mexia, João T.The STATIS (Structuration des Tableaux a Trois Indices de la Statistique) methodology is a data analysis technique which computes Euclidean distances between studies of the same observations obtained in k different circumstances. The Escoufier operators are used to obtain a geometrical representation for the studies in a series. In this study we present developments in the STATIS methodology, namely how to make...
An innovative approach to estimate infection by COVID-19
Oliveira, Manuela; Garção, Eugénio; Grilo, Luís M.; Alexandre, Armando; Mexia, João T.Given that individuals in a certain population are different (among other things they have a different immune system), it is possible that some are infected with the known virus COVID-19 and are asymptomatic and therefore not diagnosed with the disease. Thus, estimates of the number of infected and dead with COVID-19 may not correspond to reality. This study seeks to indicate a procedure to estimate the number ...
Multi-alphabetic hypercubes
Francisco, Carla; Mexia, João T.; Oliveira, Manuela; Carvalho, FranciscoThese hypercubes generalize the well-known Graeco-Latin squares. In one dimension m hypercube we have pm 'points' with m coordinates taking the values 0; 1; : : : ; p 1. In each point we locate letters from m distinct alphabets. When we vary one of the coordinates, we get all the letters of each of the alphabets. We show, how to use vector spaces over Galois Fields to obtain such hypercubes. Moreover, these hyp...
Estimation in additive models and ANOVA-like applications
Antunes, Patrícia; Ferreira, Sandra S.; Ferreira, Dário; Nunes, Célia; Mexia, João T.A well-known property of cumulant generating function is used to estimate the first four order cumulants, using least-squares estimators. In the case of additive models, empirical best linear unbiased predictors are also obtained. Pairs of independent and identically distributed models associated with the treatments of a base design are used to obtain unbiased estimators for the fourth-order cumulants. An appli...
Multiple Additive Models
Antunes, Patrícia; Ferreira, Sandra S.; Ferreira, Dário; Mexia, João T.The models constituting a multiple model will correspond to d treatments of a base design. Using a classic result on cumulant generation function we show how to obtain least square estimators for cumulants and generalized least squares estimators for vectors \beta, l=1,...,d, in the individual models. Next we carry out ANOVA-like analysis for the action of the factors in the base design. This is possible since ...
Considering the sample sizes as truncated Poisson random variables in mixed eff...
Nunes, Célia; Moreira, Elsa E.; Ferreira, Sandra S.; Ferreira, Dário; Mexia, João T.When applying analysis of variance, the sample sizes may not be previously known, so it is more appropriate to consider them as realizations of random variables. A motivating example is the collection of observations during a fixed time span in a study comparing, for example, several pathologies of patients arriving at a hospital. This paper extends the theory of analysis of variance to those situations conside...
Chisquared and related inducing pivot variables: an application to orthogonal m...
Ferreira, Dário; Ferreira, Sandra S.; Nunes, Célia; Fonseca, Miguel; Mexia, João T.We use chi-squared and related pivot variables to induce probability measures for model parameters, obtaining some results that will be useful on the induced densities. As illustration we considered mixed models with balanced cross nesting and used the algebraic structure to derive confidence intervals for the variance components. A numerical application is presented.
Random sample sizes in orthogonal mixed models with stability
Nunes, Célia; Mário, Anacleto César Xavier; Ferreira, Dário; Ferreira, Sandra S.; Mexia, João T.In this work, we presente a new approach that considers orthogonal mixed models, under situations of stability, when the sample dimensions are not known in advande. In this case, samples are considered realizations of independente rendom variables. We apply this methodology to the case where there is na upper bound for the sample dimensions, which may not be attained since failures may occur. Based on this, we ...