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- Exact critical values for one-way fixed effects models with random sample sizesPublication . Nunes, Célia; Capistrano, Gilberto; Ferreira, Dário; Ferreira, Sandra S.; Mexia, João T.Analysis of variance (ANOVA) is one of the most frequently used statistical analyses in several research areas, namely in medical research. Despite its wide use, it has been applied assuming that sample dimensions are known. In this work we aim to carry out ANOVA like analysis of one-way fixed effects models, to situations where the samples sizes may not be previously known. In these situations it is more appropriate to consider the sample sizes as realizations of independent random variables. This approach must be based on an adequate choice of the distributions of the samples sizes. We assume the Poisson distribution when the occurrence of observations corresponds to a counting process. The Binomial distribution is the proper choice if we have observations failures and there exist an upper bound for the sample sizes. We also show how to carry out our main goal by computing correct critical values. The applicability of the proposed approach is illustrated considering a real data example on cancer registries. The results obtained suggested that false rejections may be avoided by applying our approach.
- Multiple Additive ModelsPublication . 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 the estimators \tilde{\beta }(l) of \beta (l). l=1,...,d, have, approximately, the same covariance matrix. The eigenvectors of that matrix will give the principal estimable functions \epsilon_{i}^{\top} \beta (l) i=1,...,k, l=1,...,d, for the individual models. The ANOVA-like analysis will consider homologue components on principal estimable functions. To apply our results we assume the factors in the base design to have fixed effects. Moreover if w=1, and Z(1) has covariance matrix \sigma^{2} \m I_{n}, our treatment generalizes that previously given for multiple regression designs. In them we have a linear regression for each treatment of a base design. We then study the action of the factors on that design on the vectors \beta(l), l=1,...,d. An example of application of the proposed methodology is given.
- One-way fixed effects ANOVA with missing observationsPublication . Nunes, Célia; Capistrano, Gilberto; Ferreira, Dário; Ferreira, Sandra S.; Mexia, João T.The aim of this paper is to extend the theory of F-tests with random sample sizes to situations when missing observations may occur. We consider the one-way ANOVA with fixed effects. This approach is illustrated through an application to patients affected by melanoma skin cancer, from three different states of Brazil.
- 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.