Confidence regions for variance components using inducing pivot variables

The goal of this paper is to present what we think to be an interesting development of the concept of pivot variable. The inducing pivot variables induce probability measures which may be used to carry out inference. As illustration of this approach we will show how to obtain confidence intervals for the variance components of mixed linear models.info:eu-repo/semantics/publishedVersio

Linear and quadratic sufficiency and commutativity

Given a mixed model let T be the orthogonal projection matrix on the range space spanned by the mean vector. [...]info:eu-repo/semantics/publishedVersio

Inducing pivot variables and non-centrality parameters in elliptical distributions

We used inducing pivot variables to derive confidence intervals for the non-centrality parameters of samples with elliptical errors. A numerical application is presented.info:eu-repo/semantics/publishedVersio

Estimability of variance components when all model matrices commute

This work was partially supported by national funds of FCT - Foundation for Science and Technology under UID/MAT/00212/2013.This paper deals with estimability of variance components in mixed models when all model matrices commute. In this situation, it is well known that the best linear unbiased estimators of fixed effects are the ordinary least squares estimators. If, in addition, the family of possible variance-covariance matrices forms an orthogonal block structure, then there are the same number of variance components as strata, and the variance components are all estimable if and only if there are non-zero residual degrees of freedom in each stratum. We investigate the case where the family of possible variance-covariance matrices, while still commutative, no longer forms an orthogonal block structure. Now the variance components may or may not all be estimable, but there is no clear link with residual degrees of freedom. Whether or not they are all estimable, there may or may not be uniformly best unbiased quadratic estimators of those that are estimable. Examples are given to demonstrate all four possibilities.PostprintPeer reviewe

Limit distributions for asymptotically linear statistics with spherical error

The aim of this work is to obtain general results for the limit distributions of asymptotically linear statistics when the error is spherical, increasing non-centrality. These results apply directly to homoscedastic normal error thus to high precision measurements. We present a numerical example on cylinder volume to illustrate the usefulness of our approach.info:eu-repo/semantics/publishedVersio

Estimation in mixed models through three step minimization

The aim of this article is to present an estimation procedure for both fixed effects and variance components in linear mixed models. This procedure consists of a maximum likelihood method which we call Three Step Minimization, TSM. The major contribution of this method is that when variances tend to be null standard algorithms behave badly, unlike the TSM method, which uses a grid search algorithm in a compact set. A numerical application with real and simulated data is provided.info:eu-repo/semantics/publishedVersio

Tests and relevancies for the hypotheses of an orthogonal family in a model with orthogonal block structure

A model has an orthogonal block structure if it has, as covariance matrix, a linear combination of pairwise orthogonal projection matrices, that add up to the iden- tity matrix. The range space of these matrices are associated to hypotheses of an orthogonal family. In this paper we show how to obtain tests for these hypotheses when normality is assumed and how to consider their relevance when normality is discarded. Besides the notion of relevance, we formulate hypotheses in a general way that may be applied to models with orthogonal block structure, whose factors may have xed and/or random e ects. The results are applied to prime basis factorial models and an example is presented.info:eu-repo/semantics/publishedVersio

Early communication indicator: an analysis with three Portuguese toddlers

Professionals need efficient tools in early childhood communication development to identify infants and toddlers who are at risk of communication disorders or language delays. In Portugal, this project was carried out to respond to these needs due to a lack of these resources and a high prevalence of children at risk for communication problems at early ages. This paper describes the first steps to adapt the Early Communication Indicator (ECI) for the Portuguese population. The ECI is a play-based expressive communication measure for infants and toddlers aged 6 to 42 months. The ECI was originally developed in the U.S. and was designed for use by service providers to provide information about growth in communication, to help in intervention decision making, and to be administered in any language. This paper analyzes the ECI results of three Portuguese children in relation to their communication progression, based on a one-year longitudinal study. The ECI was administered when children were 17, 24, and 30 months of age. The ECI results showed that two of the children follow the typical progression of communication acquisition, with acquisition of earlier prelinguistic skills preceding growth in spoken language. The ECI results for the other child showed a very different and slower progression in the communication skills. The data obtained provided just an initial demonstration of the use of the ECI with Portuguese children. More research is needed into the development of the ECI in the Portuguese context, such as the development of a nationally representative, normative sample. Therefore, a discussion of what is needed in research and practice to advance this project is provided.Los profesionales necesitan herramientas eficaces en el desarrollo de la comunicación en la primera infancia para identificar a los bebés y niños pequeños que corren el riesgo de sufrir trastornos de la comunicación o retrasos en el lenguaje. En Portugal, este estudio se llevó a cabo para responder a estas necesidades debido a la falta de estos recursos y a una alta prevalencia de niños con riesgo de problemas de comunicación a edades tempranas. Este trabajo describe los primeros pasos para adaptar el Indicador de Comunicación Temprana (ECI) a la población portuguesa. El ECI es una medida de comunicación expresiva basada en el juego para bebés y niños pequeños de 6 a 42 meses. El ECI fue desarrollado originalmente en los EE.UU. y fue diseñado para ser utilizado por los proveedores de servicios para proporcionar información sobre el crecimiento en la comunicación, para ayudar en la toma de decisiones de intervención, y para ser administrado en cualquier idioma. Este trabajo analiza los resultados del ECI de tres niños portugueses en relación con su progresión comunicativa, basándose en un estudio longitudinal de un año. La ECI se administró cuando los niños tenían 17, 24 y 30 meses de edad. Los resultados del ECI mostraron que dos de los niños seguían la progresión típica de la adquisición de la comunicación, con la adquisición de habilidades prelingüísticas anteriores al crecimiento del lenguaje hablado. Los resultados de la ECI del otro niño mostraron una progresión muy diferente y más lenta en las habilidades comunicativas. Los datos obtenidos proporcionaron sólo una demostración inicial del uso de la ECI con niños portugueses. Se necesita más investigación sobre el desarrollo de la ECI en el contexto portugués, como el desarrollo de una muestra normativa representativa a nivel nacional. Por lo tanto, se presenta una discusión sobre lo que se necesita en la investigación y en la práctica para avanzar en la línea que marca este estudio.This work was supported by the Portuguese Funding Agency for Science and Technology (FCT) under the reference SFRH/ BD/138965/2018, within the framework of CIEC (Research Centre on Child Studies, Institute of Education, University of Minho), projects under the references UIDB/00317/2020 and UIDP/00317/2020, and CIEd (Research Centre on Education, Institute of Education, University of Minho), projects under the references UIDB/01661/2020 and UIDP/01661/2020, through national funds of FCT/MCTES-PT

Estimation and Orthogonal Block Structure

Estimators with good behaviors for estimable vectors and variance components are obtained for a class of models that contains the well known models with orthogonal block structure, OBS, see [15], [16] and [1], [2]. The study observations of these estimators uses commutative Jordan Algebras, CJA, and extends the one given for a more restricted class of models, the models with commutative orthogonal block structure, COBS, in which the orthogonal projection matrix on the space spanned by the means vector commute with all variance-covariance matrices, see [7].info:eu-repo/semantics/publishedVersio

Estimation in additive models and ANOVA-like applications

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 application to real data is presented, showing the good behaviour of the least-squares estimators and the great flexibility of our approach.info:eu-repo/semantics/publishedVersio