A new test for the mean vector in high dimensional setting

Behzad Aalipur Hafshejani, University of Texas at El Paso


Traditional statistical data analysis mostly includes methods and techniques to deal with problems in which there are many observations but a few variables. Nonetheless, the current inclination is toward more observations but also, toward more variables. Today’s observations gathered on individuals are images, curves, or even movies. Unfortunately many traditional methods do not work well in high dimensional settings. As an example Hotelling’s test which is well known and widely used in the literature does not work when it comes to high dimensional problems. Consequently statisticians are making an effort to find remedies or new approaches to multivariate mean testing. The issue with Hotelling’s test in high dimensions is that the sample covariance matrix is no longer invertible and hence the test statistic is unattainable. Alternative methods of estimating the covariance matrix have been fruitful. However, some approaches took another path. These approaches try to avoid estimating the covariance matrix. Theses approaches mainly take advantage of density approximations. Approximation of the statistics is considered and the asymptotic behavior is studied. We consider an approximation which is known to perform well in symmetrizing distributions, and we develop a new test statistic which has better power in simulations. Our results are compared with some well known tests in the literature.

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Recommended Citation

Aalipur Hafshejani, Behzad, "A new test for the mean vector in high dimensional setting" (2016). ETD Collection for University of Texas, El Paso. AAI10118216.