Miguel Fonseca

Jordan algebras, generating pivot variables and orthogonal normal models

Abstract Jordan algebras are used to present normal orthogonal models in a canonical form. It is shown that the usual factor based formulation of such models may, many times, be obtained imposing restrictions on the parameters of the canonical formulation, and examples are presented. The canonical model formulation is interesting since it leads to complete sufficient statistics. These statistics may be used to obtain pivot variables that induce probability measures in the parameter space. Monte Carlo generated samples, of arbitrary size, may be obtained having the induced probability measures. These samples may be screened so that the restrictions corresponding to the direct model formulations hold. Inference is presented using such samples.

Linear Models with Doubly Exchangeable Distributed Errors

We study the general linear model (GLM) with doubly exchangeable distributed error for m observed random variables. The doubly exchangeable general linear model (DEGLM) arises when the m-dimensional error vectors are “doubly exchangeable,” jointly normally distributed, which is a much weaker assumption than the independent and identically distributed error vectors as in the case of GLM or classical GLM (CGLM). We estimate the parameters in the model and also find their distributions. We show that the tests of intercept and slope are possible in DEGLM as a particular case using parametric bootstrap as well as multivariate Satterthwaite approximation.

Solid waste prevention and management at green festivals: A case study of the Andanças Festival, Portugal

Research on waste prevention and management at green festivals is scarce. The present study helps to fill this gap by analyzing waste prevention/reduction and management measures implemented at the Andanças festival, Portugal. Waste characterization campaigns and a questionnaire survey were conducted during the festival. The results show that the largest amount of waste generated was residual waste, followed by food and kitchen waste and packaging waste. The amount of waste generated per person per day at the festival was lower than that of other festivals for both the entire venue and the canteen. Concerning food and kitchen waste generated at the canteen, the amounts are in accordance with the findings of previous studies, but the amount of the edible fraction is comparatively low. Source separation rates are high, in line with other festivals that engage in food-waste source separation. Factors affecting the participation of attendees in waste prevention measures at the festival are the type of participant, their region of origin, the frequency of visits, and whether they are attending as a family. Efforts must be made to increase the awareness of attendees about waste prevention measures, to develop guidelines and methods to quantify the waste prevention measures, and to formulate policies aimed at increasing the application of the zero-waste principle at festivals.

Optimal estimation for doubly multivariate data in blocked compound symmetric covariance structure

The paper deals with the best unbiased estimators of the blocked compound symmetric covariance structure for m -variate observations over u sites under the assumption of multivariate normality. The free-coordinate approach is used to prove that the quadratic estimation of covariance parameters is equivalent to linear estimation with a properly defined inner product in the space of symmetric matrices. Complete statistics are then derived to prove that the estimators are best unbiased. Finally, strong consistency is proven. The proposed method is implemented with a real data set.

Tolerance intervals in a two-way nested model with mixed or random effects

We address the problem of deriving a one-sided tolerance interval in a two-way nested model with mixed or random effects. The generalized confidence interval idea is used in the derivation of our tolerance limit, and the results are obtained by suitably modifying the approach in Krishnamoorthy and Mathew [Krishnamoorthy, K. and Mathew, T., 2004, Generalized confidence limits and one-sided tolerance limits in balanced and unbalanced one-way random models. Technometrics, 46, 44–52], for the one-way random model. Our proposed tolerance limit can be estimated by Monte Carlo simulation. We have also been able to develop closed form approximations in some cases. The performance of our tolerance interval is numerically investigated and found to be satisfactory. The results are illustrated with an example.

Analysis of the influence of the variable size on the characteristics and behavior of meningiomas

Seventy-two patients submitted to meningioma surgery at Pedro Hispano Hospital from 1997 to 2001 were reviewed to analyze the association between size (largest diameter of the lesion obtained from imaging examinations) and other variables regarding the biological behavior and clinical outcome of these patients. Statistically significant associations were found between tumor size and location, type of first symptom, type of physical examination, histological grade, surgical complications, postoperative CSF bursae and the need for blood transfusion. Patients age, gender, duration of first symptom, clinical status at discharge and persistent complaints were not associated to tumor size. There was a trend towards a statistically significant association between tumor size and both grade of resection and persistent deficits. The causes and implications of the findings are discussed. Tumor size is a parameter that may interfere with the neurosurgeons capacity to treat these patients as well as with their recovery.

Estimation and incommutativity in mixed models

Abstract In this paper we present a treatment for the estimation of variance components and estimable vectors in linear mixed models in which the relation matrices may not commute. To overcome this difficulty, we partition the mixed model in sub-models using orthogonal matrices. In addition, we obtain confidence regions and derive tests of hypothesis for the variance components. A numerical example is included. There we illustrate the estimation of the variance components using our treatment and compare the obtained estimates with the ones obtained by the ANOVA method. Besides this, we also present the restricted and unrestricted maximum likelihood estimates.

Delta Method, Moment Convergence, and Inference

Statistics, as functions of the observations, are usually given by well-behaved functions. This fact is used to obtain limit distributions for statistics whose components are given by asymptotically linear functions. These results are then extended to the moments of distributions, covariance matrices and confidence regions for parameters of interest. These regions may be used to test, through duality, hypothesis on these parameters. A theoretical application is presented.

Chisquared and Related Inducing Pivot Variables: An application to Orthogonal Mixed Models

Abstract 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.

Delta Method and Moment Convergence

Statistics, either univariate or multivariate, are usually given by well‐behaved functions. This fact is used to obtain limit distributions for multivariate statistics whose components are given by asymptotically linear functions (see [1]). These results are then extended to the moments of distributions.