Profile identification via weighted related metric scaling : an application to dependent Spanish children

Disability and dependency (lack of autonomy in performing common everyday actions) affect health status and quality of life, therefore they are significant public health issues. The main purpose of this study is to establish the existing relationship among different variables (continuous, categorical and binary) referred to children between 3 and 6 years old and their functional dependence in basic activities of daily living. We combine different types of information via weighted related metric scaling to obtain homogeneous profiles for dependent Spanish children. The redundant information between groups of variables is modeled with an interaction parameter that can be optimized according to several criteria. In this paper, the goal is to obtain maximum explained variability in an Euclidean configuration. Data comes from the Survey about Disabilities, Personal Autonomy and Dependence Situations, EDAD 2008, (Spanish National Institute of Statistics, 2008)ADL, Disability, Mixed-type data, Public health, Related metric scaling

Shape theory via polar decomposition

This work proposes a new model in the context of statistical theory of shape, based on the polar decomposition. The non isotropic noncentral elliptical shape distributions via polar decomposition is derived in the context of zonal polynomials, avoiding the invariant polynomials and the open problems for their computation. The new polar shape distributions are easily computable and then the inference procedure can be studied under exact densities. As an example of the technique, a classical application in Biology is studied under three models, the usual Gaussian and two non normal Kotz models; the best model is selected by a modified BIC criterion, then a test for equality in polar shapes is performed.Comment: 14 page

Multivariate medians and measure-symmetrization

We discuss two research areas dealing respectively with (1) a class of multivariate medians and (2) a symmetrization algorithm for probability measures.Comment: Published at http://dx.doi.org/10.1214/074921707000000201 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

A Note on Rate of Convergence in Probability to Semicircular Law

In the present paper, we prove that under the assumption of the finite sixth moment for elements of a Wigner matrix, the convergence rate of its empirical spectral distribution to the Wigner semicircular law in probability is $O(n^{-1/2})$ when the dimension $n$ tends to infinity.Comment: 13 page

Regression analysis with compositional data containing zero values

Regression analysis with compositional data containing zero valuesComment: The paper has been accepted for publication in the Chilean Journal of Statistics. It consists of 12 pages with 4 figure