2017/03/01 by Alexandre Belloni, Victor Chernozhukov, Belloni, Alexandre +3 · 1 citation
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Monetary Policy and Economic Impact #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1703.00469
openalex publication_date 2017/03/01 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
We study high-dimensional linear models with error-in-variables. Such models\nare motivated by various applications in econometrics, finance and genetics.\nThese models are challenging because of the need to account for measurement\nerrors to avoid non-vanishing biases in addition to handle the high\ndimensionality of the parameters. A recent growing literature has proposed\nvarious estimators that achieve good rates of convergence. Our main\ncontribution complements this literature with the construction of simultaneous\nconfidence regions for the parameters of interest in such high-dimensional\nlinear models with error-in-variables.\n These confidence regions are based on the construction of moment conditions\nthat have an additional orthogonal property with respect to nuisance\nparameters. We provide a construction that requires us to estimate an\nadditional high-dimensional linear model with error-in-variables for each\ncomponent of interest. We use a multiplier bootstrap to compute critical values\nfor simultaneous confidence intervals for a subset S of the components. We\nshow its validity despite of possible model selection mistakes, and allowing\nfor the cardinality of S to be larger than the sample size.\n We apply and discuss the implications of our results to two examples and\nconduct Monte Carlo simulations to illustrate the performance of the proposed\nprocedure.\n