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Research Seminar Series in Statistics and Mathematics

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

Type Lecture / discussion
SpeakerNestor Parolya (Institute of Statistics, Leibniz University Hannover)
Organizer Institut für Statistik und Mathematik

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://­math/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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