Please use this identifier to cite or link to this item:
Belloni, Alexandre
Chernozhukov, Victor
Kato, Kengo
Year of Publication: 
Series/Report no.: 
cemmap working paper, Centre for Microdata Methods and Practice CWP51/14
We develop uniformly valid confidence regions for regression coefficients in a highdimensional sparse median regression model with homoscedastic errors. Our methods are based on a moment equation that is immunized against non-regular estimation of the nuisance part of the median regression function by using Neyman's orthogonalization. We establish that the resulting instrumental median regression estimator of a target regression coefficient is asymptotically normally distributed uniformly with respect to the underlying sparse model and is semiparametrically efficient. We also generalize our method to a general non-smooth Z-estimation framework with the number of target parameters p1 being possibly much larger than the sample size n. We extend Huber's results on asymptotic normality to this setting, demonstrating uniform asymptotic normality of the proposed estimators over p1-dimensional rectangles, constructing simultaneous confidence bands on all of the p1 target parameters, and establishing asymptotic validity of the bands uniformly over underlying approximately sparse models.
Post-selection inference
Neyman's Orthogonal Score test
Uniformly valid inference
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

Files in This Item:

Items in EconStor are protected by copyright, with all rights reserved, unless otherwise indicated.