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Title: Weighted $l_1$-penalized corrected quantile regression for high-dimensional temporally dependent measurement errors Authors:  Nilanjan Chakraborty - Washington University in Saint Louis (United States) [presenting]
Monika Bhattacharjee - IIT Bombay (India)
Hira Lal Koul - Michigan State University (United States)
Abstract: The focus is on a high dimensional quantile regression model in presence of measurement errors. We consider as parse high-dimensional errors-in-variables linear regression model, where measurement errors in the covariates are assumed to have linear stationary temporal dependence and known Laplace marginal distributions. The regression errors are assumed to be independent-identically distributed random variables and have non-sub-Gaussian tails. Convergence results of the weighted $l_1$-penalized corrected quantile estimator of the regression parameter vector are established. An appropriate data-adaptive algorithm is given for obtaining a suitable choice of weights. Model consistency is established for the adaptive estimator. A simulation study has also been conducted to assess the finite sample performance of the proposed estimator.