# Martin Nilsson: A shrinkage test for large-dimensional covariance matrix

Time: Wed 2021-09-08 09.00 - 09.45

Respondent: Martin Nilsson

Supervisor: Taras Bodnar

Abstract: In this thesis, we use an optimal linear shrinkage estimator for the covariance matrix along with modern results on linear spectral statistics to establish a new test for sphericity under the large-dimensional asymptotics, namely when both the number of variables p and the sample size n tend to infinity such that $$\frac{p}{n} \to c > 0$$. Using similar techniques, we also show that a previously established test based on the Cauchy–Schwarz inequality remains usable under weaker assumptions than originally stated. We perform a Monte Carlo simulation study to verify our results, to assess the quality of our new test, and to see how well it performs compared to other tests.

The report will be available on Masterarbeten i matematisk statistik 2021 .

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