Uniformly valid post-regularization confidence regions for many functional parameters in z-estimation framework
Name
nihms-1008366.pdf
Description
Accepted version
Size
707.2 KB
Format
Adobe PDF
Checksum (MD5)
e146360265eabd53e82bf7003e2373ca
Author(s)
Belloni, Alexandre
Chernozhukov, Victor V
Chetverikov, Denis
Wei, Ying
Date Issued
September 2018
Journal
Annals of statistics
Publisher
Institute of Mathematical Statistics
Citation
Belloni, Alexandre et al. "Uniformly valid post-regularization confidence regions for many functional parameters in z-estimation framework." Annals of statistics 46, 6B (September 2018): 3643-3675 © 2019 Project Euclid
Version
Author's final manuscript
Abstract
In this paper, we develop procedures to construct simultaneous confidence bands for p potentially infinite-dimensional parameters after model selection for general moment condition models where p is potentially much larger than the sample size of available data, n. This allows us to cover settings with functional response data where each of the p parameters is a function. The procedure is based on the construction of score functions that satisfy Neyman orthogonality condition approximately. The proposed simultaneous confidence bands rely on uniform central limit theorems for high-dimensional vectors (and not on Donsker arguments as we allow for p n). To construct the bands, we employ a multiplier bootstrap procedure which is computationally efficient as it only involves resampling the estimated score functions (and does not require resolving the high-dimensional optimization problems). We formally apply the general theory to inference on regression coefficient process in the distribution regression model with a logistic link, where two implementations are analyzed in detail. Simulations and an application to real data are provided to help illustrate the applicability of the results. Keyword: Inference after model selection ; moment condition models with a continuum of target parameters ; Lasso and Post-Lasso with functional response data
Subjects
Statistics, Probability and Uncertainty
Statistics and Probability
MIT Department
Massachusetts Institute of Technology. Operations Research Center
Massachusetts Institute of Technology. Department of Economics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1214/17-aos1671
