Journal
STATISTICS IN MEDICINE
Volume 40, Issue 13, Pages 3153-3166Publisher
WILEY
DOI: 10.1002/sim.8968
Keywords
consistent test; curse of dimensionality; dimensionality reduction; empirical process; integrated condition moment; uncountable moments restriction
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Funding
- National Natural Science Foundation of China [11871294]
- NSF [DMS-1620898]
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We evaluate the validity of a projection-based test for linear models when the number of covariates tends to infinity, showing that the test remains consistent and derives asymptotic distributions under the null and alternative hypotheses. The test gains dimension reduction significantly and demonstrates remarkable numerical performance, with asymptotic properties similar to when the number of covariates is fixed as long as p/n -> 0.
We evaluate the validity of a projection-based test checking linear models when the number of covariates tends to infinity, and analyze two gene expression datasets. We show that the test is still consistent and derive the asymptotic distributions under the null and alternative hypotheses. The asymptotic properties are almost the same as those when the number of covariates is fixed as long as p/n -> 0 with additional mild assumptions. The test dramatically gains dimension reduction, and its numerical performance is remarkable.
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