Seminar Teorija verovatnoća i matematička statistika, 21. jun 2018.

Naredni sastanak Seminara biće održan u četvrtak, 21. juna 2018. u sali 830 Matematičkog fakulteta sa početkom u 16 časova.

Predavač: Jelena Bradić, University of California, San Diego

Naslov predavanja: BREAKING THE CURSE OF DIMENSIONALITY IN LINEAR REGRESSION

Apstrakt: In high-dimensional linear models, the sparsity assumption is typically made, stating that most of the parameters are equal to zero. Under the sparsity assumption, estimation and, recently, inference have been well studied. However, in practice, sparsity assumption is not checkable and more importantly is often violated; a large number of covariates might be expected to be associated with the response, indicating that possibly all, rather than just a few, parameters are non-zero. A natural example is a genome-wide gene expression profiling where all genes are believed to affect a common disease marker. We show that existing inferential methods are sensitive to the sparsity assumption, and may, in turn, result in the severe lack of control of Type-I error. In this article, we propose a new inferential method, named CorrT, which is robust to model misspecification such as heteroscedasticity and lack of sparsity. CorrT is shown to have Type I error approaching the nominal level for any models and Type II error approaching zero for sparse and many dense models.   In fact, CorrT is also shown to be optimal in a variety of frameworks: sparse, non-sparse and hybrid models where sparse and dense signals are mixed. Numerical experiments show a favourable performance of the CorrT test compared to the state-of-the-art methods.

Obaveštenje se može videti i na strani http://www.stat.matf.bg.ac.rs/srpski.htm



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