Jackknife empirical likelihood test for high-dimensional regression coefficients. (English) Zbl 1468.62226
Summary: A novel way to test coefficients in high-dimensional linear regression model is presented. Under the ‘large \(p\) small \(n\)’ situation, the traditional methods, like \(F\)-test and \(t\)-test, are unsuitable or undefined. The proposed jackknife empirical likelihood test has an asymptotic chi-square distribution and the conditions are much weaker than those in the existing methods. Moreover, an extension of the proposed method can test part of the regression coefficients, which is practical in considering the significance for a subset of covariates. Simulations show that the proposed test has a good control of the type-I error, and is more powerful than P.-S. Zhong and S. X. Chen’s [J. Am. Stat. Assoc. 106, No. 493, 260–274 (2011; Zbl 1396.62110)] method in most cases. The proposed test is employed to analyze a rheumatoid arthritis data to find the association between rheumatoid arthritis and the SNPs on the chromosomes 6.
MSC:
| 62-08 | Computational methods for problems pertaining to statistics |
| 62H15 | Hypothesis testing in multivariate analysis |
| 62J05 | Linear regression; mixed models |
Keywords:
jackknife empirical likelihood; high-dimensional analysis; regression coefficients; partial test with nuisance parameter; power; type-I error rateCitations:
Zbl 1396.62110References:
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