Research Seminar Series in Statistics and Mathematics

Wirtschaftsuniversität Wien, Departments 4 D4.4.00809:00 - 10:10

Art Vortrag/Diskussion
Vortragende/rNestor Parolya (Institute of Statistics, Leibniz University Hannover)
Veranstalter Institut für Statistik und Mathematik
Kontakt katrin.artner@wu.ac.at

Nestor Parolya (Insti­tute of Statis­tics, Leibniz Univer­sity Hannover) about "Testing for Inde­pen­dence of Large Dimen­sional Vectors"

The Insti­tute for Statis­tics and Mathe­ma­tics (Depart­ment of Finance, Accoun­ting and Statis­tics) cordi­ally invites ever­yone inte­rested to attend the talks in our Rese­arch Seminar Series, where inter­na­tio­nally renowned scho­lars from leading univer­si­ties present and discuss their (working) papers.

The list of talks for the winter term 2018/19 is avail­able via the follo­wing link: https://www.wu.ac.at/en/stat­math/resse­minar

In this paper new tests for the inde­pen­dence of two high-­di­men­sional vectors are inves­ti­gated. We consider the case where the dimen­sion of the vectors increases with the sample size and propose multi­va­riate analysis of vari­an­ce-­type statis­tics for the hypo­thesis of a block diagonal cova­ri­ance matrix. The asym­ptotic proper­ties of the new test statis­tics are inves­ti­gated under the null hypo­thesis and the alter­na­tive hypo­thesis using random matrix theory. For this purpose we study the weak conver­gence of linear spec­tral statis­tics of central and (condi­tio­nally) non-­cen­tral Fisher matrices. In parti­cular, a central limit theorem for linear spec­tral statis­tics of large dimen­sional (condi­tio­nally) non-­cen­tral Fisher matrices is derived which is then used to analyse the power of the tests under the alter­na­tive.
The theo­re­tical results are illus­trated by means of a simu­la­tion study where we also compare the new tests with several alter­na­tive, in parti­cular with the commonly used corrected likelihood ratio test. It is demons­trated that the latter test does not keep its nominal level, if the dimen­sion of one sub-vector is rela­tively small compared to the dimen­sion of the other sub-vector. On the other hand the tests proposed in this paper provide a reasonable appro­xi­ma­tion of the nominal level in such situa­tions. More­over, we observe that one of the proposed tests is most powerful under a variety of corre­la­tion scena­rios.

Kindly note that on November 9 two talks are sche­duled at our insti­tute:
9:00 – 10:10  Nestor Parolya (Leibniz Univer­sity Hannover)
11:00 – 12:10  Tobias Fissler (Impe­rial College London)

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