Abstract
The Watson distribution defined on the hypersphere is one of the most used distributions for modelling axial data. In this paper, we consider the discriminant analysis for axial data assumed to come from a mixture of Watson distributions defined on the hypersphere. We develop an optimal classification rule, which enables us to assign a new observation into one of several Watson subpopulations defined on the hypersphere. As the probabilities of misclassification cannot be calculated in closed form, we report on a simulation study to estimate, in some cases, the probabilities of misclassification and a distance between the two Watson subpopulations defined on the hypersphere. An illustration of our approach is provided using data defined on the sphere given in the literature.

Abstract
We analyse the dynamics and evolution of the corporate restructuring process in the Portuguese banking sector, where 10 banks were privatised during the period 1989-1996. We apply a novel methodological approach in this context, using a multidimensional measure of restructuring that links product and labour market variables. We find evidence of considerable heterogeneity in the restructuring process, where firms adjust at different speeds and intensities. We also find that the wage level is by far the firm attribute that changed more, which is shown to reflect substantial changes in terms of composition, and not size, of the workforce. Our empirical evidence also suggests that privatisation is associated with a higher level of rent sharing. © 2011 Elsevier B.V.

Abstract
The Watson distribution is one of the most used distributions for modeling axial data. In some situations, it is important to investigate if several Watson populations differ significantly. In this paper, we develop likelihood ratio tests and the ANOVA for testing the hypothesis of the equality of the directional parameters of several Watson distributions with different concentrations. We also determine the empirical power of the ANOVA and LR tests for some dimensions of the sphere.

Abstract
The Watson distribution is frequently used for modeling axial data. We propose the two-way analysis of variance for a concentrated Watson distribution defined on the hypersphere in the girdle or bipolar form. We illustrate this technique with spherical data.

Abstract

Abstract
An important problem in directional statistics is to test the null hypothesis of a common mean direction for several populations. The Analysis of Variance (ANOVA) test for vectorial data may be used to test the hypothesis of the equality of the mean directions for several von Mises-Fisher populations. As this test is valid only for large concentrations, we propose in this paper to apply the resampling techniques of bootstrap and permutation to the ANOVA test. We carried out an extensive simulation study in order to evaluate the performance of the ANOVA test with the resampling techniques, for several sphere dimensions and different sample sizes and we compare with the usual ANOVA test for data from von Mises-Fisher populations. The purpose of this simulation study is also to investigate whether the proposed tests are preferable to the ANOVA test, for low concentrations and small samples. Finally, we present an example with spherical data.