Abstract
As the Watson distribution is frequently used for modeling axial data, it is important to investigate the existence of possible outliers in samples from this distribution. Then, we develop for the bipolar Watson distribution defined on the hypersphere, some tests of discordancy of an outlier or several outliers en bloc based on the likelihood ratio, supposing an alternative model of contamination of slippage type. We evaluate the performance of these tests of discordancy of an outlier and we also compare some tests of discordancy of an outlier available for this distribution.

Abstract
The bipolar Watson distribution is frequently used for modeling axial data. We extend the one-way analysis of variance based on this distribution to a two-way layout. We illustrate the method with directional data in three dimensions.

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.