New Trends in Probability and Statistics/Multivariate Statistics and Matrices in Statistics

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This work delves into various advanced statistical methodologies and their applications. It begins with asymptotic distributions, exploring error bounds for classification statistics and empirical spacing processes, alongside the Cornish-Fisher expansion in finite populations. The focus then shifts to general linear regression models, discussing the proportionality of regression coefficients in misspecified models, partitioned regression, and simpler tests for linear inequality constraints. It highlights the nuanced relationship between increased correlations with response variables and the coefficient of determination, including a discussion on related interpretations. The text further examines tests in multivariate statistics, presenting a projection NT-type test for spherical symmetry and applications of directional statistics in astronomy. It also covers methods for fitting circles or points to spherical data. In the realm of multivariate nonparametric models, the use of Hellinger distance in contingency table data visualization is discussed, along with bivariate generalizations of the median and distance-based regression in heliophysical data analysis. Additionally, it addresses discrimination and classification, focusing on the small sample properties of ridge estimates in classification contexts, trimmed k-means, and properties of k-variance. Lastly, the work reviews shorted matrices in linear statistical models, arra