Comparing the performance of multivariate location tests for L_p-norm distributed data
Korpela, Simo (2014)
2014
Tilastotieteen maisteriopinnot - Master's Programme in Statistics
Informaatiotieteiden yksikkö - School of Information Sciences
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Hyväksymispäivämäärä
2014-07-03
Julkaisun pysyvä osoite on
https://urn.fi/URN:NBN:fi:uta-201407102003
https://urn.fi/URN:NBN:fi:uta-201407102003
Tiivistelmä
There are plenty of tests for multivariate location around which all make slightly different assumptions. The classical parametric procedure for the one-sample location problem is Hotelling's T2 test (Hotelling, 1931) which assumes that the data is generated from a multivariate normal distribution. The test is optimal under the assumption of normality. However, the method may lead to unreliable results when the underlying distribution strongly deviates from the assumed model. As a reaction to this, the aim in research has been to develop methods that are valid under much weaker conditions than the normal-theory based Hotelling's T2. Many nonparametric methods have been developed in the literature with the objective of extending to the multivariate context the classical univariate sign and rank techniques. Different attempts to generalize the classical nonparametric sign and rank methods have led to a huge body of literature.
This thesis presents the main multivariate tests of location and reports the results of an extensive simulation study. Tests based on marginal signs and ranks (Puri and Sen, 1971), spatial signs and ranks (Oja, 2010), Oja signs and ranks (Oja, 1999), the optimal signed-rank score tests by Hallin and Paindaveine (2002a, 2002b), and tests using marginal signs and ranks in the symmetric independent component (IC) model (Nordhausen, Oja, and Paindaveine, 2009) are discussed and applied. The parametric Hotelling's T2 test serves as a reference test. The goal is to provide practical guidelines which test might be most useful in practice.
In our simulation study, the powers of the different location tests are compared under various settings, namely, under different underlying distributions, sample sizes, dimensions, and deviations from the null value. As extensions to normally distributed data, Lp-norm distributions are used as simulation data. We consider eleven different choices of underlying distributions, four different sample sizes, three different dimensions, and four different deviations from the null value. The proposed procedures are easy to implement on statistical programming languages such as R.
This thesis presents the main multivariate tests of location and reports the results of an extensive simulation study. Tests based on marginal signs and ranks (Puri and Sen, 1971), spatial signs and ranks (Oja, 2010), Oja signs and ranks (Oja, 1999), the optimal signed-rank score tests by Hallin and Paindaveine (2002a, 2002b), and tests using marginal signs and ranks in the symmetric independent component (IC) model (Nordhausen, Oja, and Paindaveine, 2009) are discussed and applied. The parametric Hotelling's T2 test serves as a reference test. The goal is to provide practical guidelines which test might be most useful in practice.
In our simulation study, the powers of the different location tests are compared under various settings, namely, under different underlying distributions, sample sizes, dimensions, and deviations from the null value. As extensions to normally distributed data, Lp-norm distributions are used as simulation data. We consider eleven different choices of underlying distributions, four different sample sizes, three different dimensions, and four different deviations from the null value. The proposed procedures are easy to implement on statistical programming languages such as R.