Berry-Esseen Bounds for Projection Parameters and Partial Correlations\n 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)

paper · pdf · doi:10.48550/arxiv.2007.09751

openalex publication_date 2020/07/19 · 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\nleast squares estimator of the projection parameters normalized by the\nsandwich-based standard errors. Our results hold in the increasing dimension\nsetting and under minimal assumptions on the data generating distribution. In\nparticular, we do not assume a linear regression function and only require the\nexistence of finitely many moments for the response and the covariates.\nFurthermore, we construct confidence sets for the projection parameters in the\nform of hyper-rectangles and establish finite sample bounds on their coverage\nand accuracy. We derive analogous results for partial correlations among the\nentries of sub-Gaussian vectors. endabstract\n

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