2025/11/12 by Shunsuke Imai, Imai, Shunsuke
Mathematics · #FOS: Mathematics #Random Matrices and Applications #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2511.08870
openalex publication_date 2025/11/12 · openalex created_date 2025/11/14 · openalex updated_date 2026/07/28
We develop Gaussian approximations for high-dimensional vectors formed by second-order U- and V-statistics whose kernels depend on sample size under independent but not identically distributed (i.n.i.d.) sampling. Our results hold irrespective of which component of the Hoeffding decomposition is dominant, thereby covering both non-degenerate and degenerate regimes as special cases. By allowing i.n.i.d.~sampling, the class of statistics we analyze includes weighted U- and V-statistics and two-sample U- and V-statistics as special cases, which cover estimators of parameters in regression models with many covariates, many-weak instruments as well as a broad class of smoothed two-sample tests and the separately exchangeable arrays, among others. In addition, we develop maximal inequalities for high-dimensional U-statistics with size-dependent kernels under the i.n.i.d.~setting, in a form that remains sharp across a broad range of applications, which may be of independent interest.