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Title: On robust estimates of sphericity in high-dimension Authors:  Esa Ollila - Aalto University (Finland) [presenting]
Elias Raninen - Aalto University (Finland)
Abstract: The need to estimate or test sphericity (i.e., that the covariance matrix is proportional to identity) arises in various applications in statistics, and thus the problem has been investigated in numerous papers, most recently in shrinkage covariance matrix estimation problems. We investigate robust estimates of sphericity, especially in a high-dimensional setting, where the data dimensionality $p$ is larger or of similar magnitude as the sample size $n$. The population measure of sphericity that we consider is defined as the ratio of the mean of the squared eigenvalues of the covariance matrix relative to the mean of its eigenvalues squared. This population quantity is then estimated using robust spatial (both symmetrized and standard) sign and rank covariance matrices as well as using robust $M$-estimators of scatter matrices. Properties of such estimators are derived and reviewed, and a simulation study is provided comparing the robust estimators of sphericity in the high-dimensional setting.