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We consider testing regression coefficients in high dimensional generalized linear models. An investigation of the test of Goeman et al. (2011) is conducted, which reveals that if the inverse of the link function is unbounded, the high dimensionality in the covariates can impose adverse impacts on the power of the test. We propose a test formation which can avoid the adverse impact of the high dimensionality. When the inverse of the link function is bounded such as the logistic or probit regression, the proposed test is as good as Goeman et al. (2011)s test. The proposed tests provide p-values for testing significance for gene-sets as demonstrated in a case study on an acute lymphoblastic leukemia dataset.
The focus of modern biomedical studies has gradually shifted to explanation and estimation of joint effects of high dimensional predictors on disease risks. Quantifying uncertainty in these estimates may provide valuable insight into prevention strat
We are interested in testing general linear hypotheses in a high-dimensional multivariate linear regression model. The framework includes many well-studied problems such as two-sample tests for equality of population means, MANOVA and others as speci
Field observations form the basis of many scientific studies, especially in ecological and social sciences. Despite efforts to conduct such surveys in a standardized way, observations can be prone to systematic measurement errors. The removal of syst
Let $(Y,(X_i)_{iinmathcal{I}})$ be a zero mean Gaussian vector and $V$ be a subset of $mathcal{I}$. Suppose we are given $n$ i.i.d. replications of the vector $(Y,X)$. We propose a new test for testing that $Y$ is independent of $(X_i)_{iin mathcal{I
For a high-dimensional linear model with a finite number of covariates measured with error, we study statistical inference on the parameters associated with the error-prone covariates, and propose a new corrected decorrelated score test and the corre