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One-way random effects ANOVA with random sample sizes: An application to a Brazilian database on cancer registries

Publication . Capistrano, Gilberto; Nunes, Célia; Ferreira, Dário; Ferreira, Sandra S.; Mexia, João T.

ANOVA is routinely used in many situations, namely in medical research, where the sample sizes may not be previously known. This leads us to consider the samples sizes as realizations of random variables. The aim of this paper is to extend one-way random effects ANOVA to those situations and apply our results to a Brazilian database on cancer registries.

2015Journal article

Open access

Inference for types and structured families of commutative orthogonal block structures

Publication . Carvalho, Francisco; Mexia, João T.; Santos, Carla; Nunes, Célia

Models with commutative orthogonal block structure, COBS, have orthogonal block structure, OBS, and their least square estimators for estimable vectors are, as it will be shown, best linear unbiased estimator, BLUE. Commutative Jordan algebras will be used to study the algebraic structure of the models and to define special types of models for which explicit expressions for the estimation of variance components are obtained. Once normality is assumed, inference using pivot variables is quite straightforward. To illustrate this class of models we will present unbalanced examples before considering families of models. When the models in a family correspond to the treatments of a base design, the family is structured. It will be shown how, under quite general conditions, the action of the factors in the base design on estimable vectors, can be studied.

2014Journal article

Open access

ANOVA with random sample sizes: An application to a Brazilian database on cancer registries

Publication . Nunes, Célia; Capistrano, Gilberto; Ferreira, Dário; Ferreira, Sandra S.

2013Journal article

Open access

Estimation of variance components in normal linear mixed models with additivity

Publication . 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.

2015Journal article

Restricted access