Title: Estimation and Inference in High Dimensional Error‐in‐Variables Models and
an Application to Microbiome Data

Abstract:
We discuss three closely related problems in high dimensional error in variables (EIV)
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 high dimensional EIV models. We show that our method provides
optimal rates of convergence with only a sub‐block of the bias correction matrix, while also
reducing the computational cost in comparison to the L1 penalized bias corrected least squares
estimator. We 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 such high dimensional
models.  All theoretical results are supported by the simulations.

Bio:

Dr. Kaul received a PhD (2015) in Statistics from Michigan State University and is currently a research fellow at the National Institute of Environmental Health Sciences (NIEHS), Biostatistics and Computational Biology Branch. Dr. Kaul has developed modern statistical methods for big data/high dimensional data with a focus on covariate selection and estimation in linear/generalized linear models.  In addition, Dr. Kaul has implemented Machine Learning techniques for the analysis of the human microbiome data.  dimensional models. All theoretical results are also supported by simulations.