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- Estimation of variance components in normal linear mixed models with additivityPublication . Ferreira, Dário; Ferreira, Sandra S.; Nunes, Célia; Mexia, João T.In this paper we use commutative Jordan Algebras to estimate variance components in linear mixed models. We apply the theory to a model in which three factors cross and one of the factors is additive to the other two.
- Confidence intervals for variance components in gauge capability studiesPublication . Ferreira, Dário; Ferreira, Sandra S.; Nunes, Célia; Oliveira, Teresa A.; Mexia, João T.We present a method, that uses pivot variables, which are functions of statistics and parameters, of constructing confidence intervals for variance components in gauge capability studies. As illustration we will consider a study on repeatability and reproducibility measures. Besides this the paper includes a simulation study demonstrating that in approximately 9500 out of 10000 simulations the 95% confidence interval covers the true value of the parameter.
- Estimation of variance components in models with positive commutativity orthogonal block structurePublication . Ferreira, Sandra S.; Ferreira, Dário; Nunes, Célia; Mexia, João T.The article addresses alternative estimators for estimable vectors. The relative performances of the proposed estimators are studied through numerical analysis. The major motivation behind this article is providing an optimal estimator through applying simple modifications in models with Orthogonal Block Structure. In addition, an illustrative example is presented to demonstrate the efficiency and accuracy of the proposed method.
- Segregation and intrinsec restrictions on canonic variance componentsPublication . Ferreira, Dário; Ferreira, Sandra S.; Nunes, Célia; Mexia, João T.This paper deals with the estimability of variance components, in mixed models, when the dimension of the commutative algebra, spanned by all possible variance-covariance matrices, is greater than the number of linearly independente unknown variance components. As example we present an application to a random three-factor crossed-model.
- Estimation in additive models and ANOVA-like applicationsPublication . 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 application to real data is presented, showing the good behaviour of the least-squares estimators and the great flexibility of our approach.