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Assessing Normality of High-Dimensional Data
Jönköping University, Jönköping International Business School, JIBS, Economics, Finance and Statistics.
Jönköping University, Jönköping International Business School, JIBS, Economics, Finance and Statistics.
2013 (English)In: Communications in statistics. Simulation and computation, ISSN 0361-0918, E-ISSN 1532-4141, Vol. 42, no 2, 360-369 p.Article in journal (Refereed) Published
Abstract [en]

The assumption of normality is crucial in many multivariate inference methods and may be even more important when the dimension of data is proportional to the sample size. It is therefore necessary that tests for multivariate non normality remain well behaved in such settings. In this article, we examine the properties of three common moment-based tests for non normality under increasing dimension asymptotics (IDA). It is demonstrated through Monte Carlo simulations that one of the tests is inconsistent under IDA and that one of them stands out as uniformly superior to the other two.

Place, publisher, year, edition, pages
2013. Vol. 42, no 2, 360-369 p.
Keyword [en]
Multivariate skewness and kurtosis, Increasing dimension, Asymptotics, Non normality
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:hj:diva-16439DOI: 10.1080/03610918.2011.636164OAI: oai:DiVA.org:hj-16439DiVA: diva2:450880
Available from: 2011-10-24 Created: 2011-10-24 Last updated: 2013-11-07Bibliographically approved
In thesis
1. Assessing Distributional Properties of High-Dimensional Data
Open this publication in new window or tab >>Assessing Distributional Properties of High-Dimensional Data
2013 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

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 cointegration

Place, publisher, year, edition, pages
Jönköping: Jönköping International Business School, 2013. 27 p.
Series
JIBS Dissertation Series, ISSN 1403-0470 ; 092
National Category
Economics and Business
Identifiers
urn:nbn:se:hj:diva-22547 (URN)978-91-86345-46-4 (ISBN)
Public defence
2013-11-29, B1014, Jönköping International Business School, Gjuterigatan 5, 10:00 (English)
Opponent
Supervisors
Available from: 2013-11-07 Created: 2013-11-07 Last updated: 2013-11-07Bibliographically approved

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