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Tests for High Dimensional Generalized Linear Models

Chen, Song Xi and Guo, Bin (2014): Tests for High Dimensional Generalized Linear Models.

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Abstract

We consider testing regression coefficients in high dimensional generalized linear models. By modifying a test statistic proposed by Goeman et al. (2011) for large but fixed dimensional settings, we propose a new test which is applicable for diverging dimension and is robust for a wide range of link functions. The power properties of the tests are evaluated under the setting of the local and fixed alternatives. A test in the presence of nuisance parameters is also proposed. The proposed tests can provide p-values for testing significance of multiple gene-sets, whose usefulness is demonstrated in a case study on an acute lymphoblastic leukemia dataset.

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