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Aspects of Moment Testing when p>n
Linnaeus University, School of Business and Economics, Department of Economics and Statistics.ORCID iD: 0000-0002-0963-0741
2018 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis concerns the problem of statistical hypothesis testing for mean vector as well as testing for non-normality in a high-dimensional setting which is called the Kolmogorov condition. Since we consider mainly the first and the second moment in testing for mean vector and we utilize the third and the fourth moment in testing for non-normality, this thesis concerns a more general moment testing problem. The research question is related to a data matrix with $p$ rows, which is the number of parameters and $n$ columns which is the sample size, where $p$ can exceed $n$, assuming that the ratio $\frac{p}{n}$ converges when both the number of parameters and the sample size increase. 

The first paper reviews the Dempster's non-exact test for mean vector, with a focus on one-sample case. We investigated its size and power properties compared to Hotelling's $\mathit{T}^2$ test as well as Srivastava's test using Monte Carlo simulation. 

The second paper concerns the problem of testing for multivariate non-normality in high-dimensional data. We proposed three test statistics which are based on marginal skewness and kurtosis. Simulation studies are carried out for examining the size and power properties of the three test statistics.

Abstract [sv]

Avhandlingen undersöker hypotesprövning i höga dimensioner, under förutsättning att det så kallad Kolmogorovvillkoret (Kolmogorov condition) är uppfyllt. Villkoret innerbär att antalet parametrar ökar tillsammans med storleken på stickprovet med en konstant hastighet. Till kategorin multivariat analys räknas de statistiska metoder som analyserar stickprov från flerdimensionella fördelningar, särskilt multivariat normalfördelning. För högdimensionella data fungerar klassiska skattningar av kovariansmatris inte tillfredställande eftersom komplexiteten med att skatta den inversa kovariansmatrisen ökar när dimensionen ökar. I den första uppsatsen utförs en genomgång av Dempsters (non-exact) test där skattning av den inversa kovariansmatrisen inte behövs. Istället används spåret (trace) av en kovariansmatris. I den andra uppsatsen testas antagandet om normalfördelning med hjälp av tredje och fjärde ordningens moment. Tre olika testvariabler har föreslagits där sumuleringar också presenteras för att jämföra hur väl en icke-normalfördelning identifieras av testet.

Place, publisher, year, edition, pages
Växjö: Linnaeus University Press, 2018.
Series
Lnu Licentiate ; 23/2018
Keywords [en]
High-dimensional data, Asymptotic distribution, Kolmogorov condition, Monte Carlo simulation, Hypothesis testing, Skewness and kurtosis
National Category
Probability Theory and Statistics
Research subject
Statistics/Econometrics
Identifiers
URN: urn:nbn:se:lnu:diva-79294ISBN: 978-91-88898-35-7 (print)ISBN: 978-91-88898-36-4 (electronic)OAI: oai:DiVA.org:lnu-79294DiVA, id: diva2:1272985
Presentation
2018-12-18, K1050, Hus K, Växjö, Växjö, 10:00 (English)
Opponent
Supervisors
Available from: 2018-12-27 Created: 2018-12-20 Last updated: 2019-01-18Bibliographically approved

Open Access in DiVA

Licentiate Thesis (Comprehensive Summary)(1220 kB)13 downloads
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