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Hypothesis Testing in High-Dimensional Linear Regression: A Normal Reference Scale-Invariant Test by Tianming Zhu; Liang Zhang; Jin-Ting Zhang is a Mathematics article available to read on EtoBox.

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Recently, several non-scale-invariant and scale-invariant tests have been proposed for a general linear hypothesis testing problem for high-dimensional data which includes one-way and two-way MANOVA tests as special cases. Many of these tests impose strong assumptions on the underlying covariance matrix so that their test statistics are asymptotically normally distributed. However, a simulation example and some theoretical justifications indicate that these assumptions are rarely satisfied in practice so that these tests may not be able to maintain the nominal size well. To overcome this problem, in this paper, a normal-reference scale-invariant test is proposed and studied. It has good size control and power without imposing strong assumptions on the underlying covariance or correlation matrix. A real data example and several simulation studies demonstrate that the proposed test has much better size control and power than several non-scale and scale-invariant tests.

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Author

Tianming Zhu; Liang Zhang; Jin-Ting Zhang

Publisher

Statistica Sinica (Institute of Statistical Science)

Published

2023

Language

EN

Field

Mathematics (Physical Sciences)