Berry-Esseen Bounds for Projection Parameters and Partial Correlations with Increasing Dimension

2020/07/19 by Arun Kumar Kuchibhotla, Alessandro Rinaldo, Kuchibhotla, Arun Kumar +3
Mathematics · #Advanced Statistical Methods and Models #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST) #math.ST #stat.ME #stat.TH

paper · pdf · doi:10.48550/arxiv.2007.09751

58 pages, 0 figures

openalex publication_date 2020/07/19 · arxiv created 2021/10/22 · arxiv updated 2021/10/25 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We provide finite sample bounds on the Normal approximation to the law of the least squares estimator of the projection parameters normalized by the sandwich-based standard errors. Our results hold in the increasing dimension setting and under minimal assumptions on the data generating distribution. In particular, we do not assume a linear regression function and only require the existence of finitely many moments for the response and the covariates. Furthermore, we construct confidence sets for the projection parameters in the form of hyper-rectangles and establish finite sample bounds on their coverage and accuracy. We derive analogous results for partial correlations among the entries of sub-Gaussian vectors. \endabstract

Citations

• The lower tail of random quadratic forms, with applications to ordinary least squares and restricted eigenvalue properties
• A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity
• Valid Post-selection Inference in Assumption-lean Linear Regression
• A general theory of hypothesis tests and confidence regions for sparse high dimensional models
• High-dimensional CLT for Sums of Non-degenerate Random Vectors:\n n^-1/2-rate

Related

• Inference for Projection Parameters in Linear Regression: beyond d = o(n^1/2)
• The Berry-Esseen Bound for High-dimensional Self-normalized Sums
• Central Limit Theorem and Bootstrap Approximation in High Dimensions: Near 1/√(n) Rates via Implicit Smoothing
• High-dimensional Berry-Esseen Bound for m-Dependent Random Samples
• Berry-Esseen bounds for random projections of ℓ_pⁿ-balls