Publications [#338343] of Alexandre Belloni

Papers Published

1. Belloni, A; Chernozhukov, V; Chetverikov, D; Wei, Y, UNIFORMLY VALID POST-REGULARIZATION CONFIDENCE REGIONS FOR MANY FUNCTIONAL PARAMETERS IN Z-ESTIMATION FRAMEWORK., The Annals of Statistics, vol. 46 no. 6B (December, 2018), pp. 3643-3675, Institute of Mathematical Statistics [doi]
   (last updated on 2023/06/01)

   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.