Statistics Across Campuses: Davy Paindaveine -- Testing for principal component directions under weak identifiability

Testing for principal component directions under weak identifiability 

Date: 02 October 2020, Friday 

Time: 4pm 

Speaker: Prof Davy Paindaveine (Université Libre de Bruxelles) 

Abstract: 

We consider the problem of testing the null hypothesis that the first principal
direction coincides with a given direction in the multivariate Gaussian model.  In the
classical setup where eigenvalues are fixed, the likelihood ratio test (LRT) and the Le
Cam optimal test for this problem are asymptotically equivalent under the null
hypothesis, hence also under sequences of contiguous alternatives.  We show that this
equivalence does not survive asymptotic scenarios where the ratio of both leading
eigenvalues goes to one faster than the inverse of root-n.  For such scenarios, the Le
Cam optimal test still asymptotically meets the nominal level constraint, whereas the
LRT severely overrejects the null hypothesis.  Consequently, the former test should be
favored over the latter one whenever the two largest sample eigenvalues are close to
each other.  By relying on the Le Cam’s asymptotic theory of statistical experiments, we
study the non-null and optimality properties of the Le Cam optimal test in the
aforementioned asymptotic scenarios and show that the null robustness of this test is
not obtained at the expense of power.  Our results are illustrated on a real data
example.  

Link: https://au.bbcollab.com/guest/fcf219c74ac743e89565a9e6e8d349a9