Zhang Q, Chen F, Wu S, Liang H. A simple yet powerful test for assessing goodness-of-fit of high-dimensional linear models.
Stat Med 2021;
40:3153-3166. [PMID:
33792070 DOI:
10.1002/sim.8968]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2020] [Revised: 01/16/2021] [Accepted: 03/13/2021] [Indexed: 11/06/2022]
Abstract
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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