Robust Sure Independence Screening for Non-polynomial dimensional Generalized Linear Models
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We consider the problem of variable screening in ultra-high dimensional (of non-polynomial order) generalized linear models (GLMs). Since the popular SIS approach is extremely unstable in the presence of contamination and noises, which may frequently arise in the large scale sample data (e.g., Omics data), we discuss a new robust screening procedure based on the minimum density power divergence estimator (MDPDE) of the marginal regression coefficients. Our proposed screening procedure performs extremely well both under pure and contaminated data scenarios. We also theoretically justify the use of this marginal MDPDEs for variable screening from the population as well as sample aspects; in particular, we prove that these marginal MDPDEs are uniformly consistent leading to the sure screening property of our proposed algorithm. We have also proposed an appropriate MDPDE based extension for robust conditional screening in the GLMs along with the derivation of its sure screening property.
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