Assessing Distributional Properties of High-Dimensional Data

This doctoral thesis consists of five papers in the field of multivariate statistical analysis of high-dimensional data. Because of the wide application and methodological scope, the individual papers in the thesis necessarily target a number of different statistical issues. In the first paper, Monte Carlo simulations are used to investigate a number of tests of multivariate non-normality with respect to their increasing dimension asymptotic (IDA) properties as the dimension p grows proportionally with the number of observations n such that p/n → c where is a constant. In the second paper a new test for non-normality that utilizes principal components is proposed for cases when p/n → c. The power and size of the test are examined through Monte Carlo simulations where different combinations of p and n are used. The third paper treats the problem of the relation between the second central moment of a distribution to its first raw moment. In order to make inference of the systematic relationship between mean and standard deviation, a model that captures this relationship by a slope parameter (β) is proposed and three different estimators of this parameter are developed and their consistency proven in the context where the number of variables increases proportionally to the number of observations. In the fourth paper, a Bayesian regression approach has been taken to model the relationship between the mean and standard deviation of the excess return and to test hypotheses regarding the β parameter. An empirical example involving Stockholm exchange market data is included. Then finally in the fifth paper three new methods to test for panel cointegratio