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A simple yet powerful test for assessing goodness‐of‐fit of high‐dimensional linear models
Author(s) -
Zhang Qi,
Chen Feifei,
Wu Shunyao,
Liang Hua
Publication year - 2021
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.8968
Subject(s) - covariate , goodness of fit , mathematics , simple (philosophy) , null hypothesis , dimension (graph theory) , infinity , projection (relational algebra)
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.