COLLEGE OF ARTS AND SCIENCES Department of Mathematics and Statistics


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Mathematics Colloquium: Estimation and Inference in High Dimensional Error-in-Variables Models and an Application to Microbiome Data


4:10pm Webster Hall 11

Abhishek Kaul

We discuss three closely related problems in high dimensional error in variables regression, 1.Additive measurement error in covariates, 2.Missing at random covariates and 3.Precision matrix recovery. We propose a two stage methodology that performs estimation post variable selection in such high dimensional measurement error models. We show that our method provides optimal rates of convergence with only a sub‐block of the bias correction matrix, while also providing a higher computational efficiency in comparison to available methods. We then apply the proposed method to human microbiome data, where we classify observations to geographical locations based on corresponding microbial compositions. Lastly, we provide methods for constructing confidence intervals on target parameters in these high dimensional models, our approach is based on the construction of moment conditions that have an additional orthogonality property with respect to nuisance parameters. All theoretical results are also supported by simulations. Refreshments served at 3:30 p.m. Hacker Lounge (Neill 216)