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Random sample sizes in one-way fixed effects models

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

Analysis of variance (ANOVA) is one of the most frequently used statistical analysis 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. Assuming that the samples were generated by Pois- son counting processes we obtain the unconditional distribution of the test statistic, under the assumption that we have random sample sizes. The applicability of the pro- posed approach is illustrated considering a real data example on cancer registries. The results obtained suggested that false rejections may be avoid by applying our approach.

2017Conference object

Restricted access

Orthogonal Block Structure and Uniformly Best Linear Unbiased Estimators

Publication . Ferreira, Sandra S.; Ferreira, Dário; Nunes, Célia; Carvalho, Francisco; Mexia, João T.

Models with orthogonal block structure, OBS, have variance covariance matrices that are linear combinations [...]

2019Book part

Open access

Exact critical values for one-way fixed effects models with random sample sizes

Publication . 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.

2019Journal article

Open access

The number of P-vertices in a matrix with maximum nullity

Publication . Fernandes, Rosário; Cruz, Henrique F. Da

Let T be a tree with n≥2 vertices. Set S(T) for the set of all real symmetric matrices whose graph is T. Let A∈S(T) and i∈{1,…,n} . We denote by A(i) the principal submatrix of A obtained after deleting the row and column i. We set mA(i)(0)=mA(0)+1, we say that i is a P-vertex of A. As usual, M(T) denotes the maximum nullity occurring of B∈S(T). In this paper we determine an upper bound and a lower bound for the number of P-vertices in a matrix A∈S(T)with nullity M(T). We also prove that if the integer b is between these two bounds, then there is a matrix E∈S(T) with b P-vertices and maximum nullity.

2018-06-15Journal article

Open access

Optimal Estimators in Mixed Models with Orthogonal Block Structures

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

Mixed models whose variance–covariance matrices are the positive definite linear combinations of pairwise orthogonal orthogonal projection matrices have orthogonal block structure. Here, we will obtain uniformly minimum-variance unbiased estimators for the relevant parameters when normality is assumed and we show that those for estimable vectors are, in general, uniformly best linear unbiased estimators. This is, they are best linear unbiased estimators whatever the variance components.

2018Book part

Restricted access