Mengtao Wen | Searcharxiv

arXiv2026

Elliptical Regularized Hotelling Tests for High-Dimensional Change-Point Detection

We propose an elliptical regularized Hotelling (ERHT) procedure for detecting location changes in high-dimensional sequences with heavy-tailed, cross-sectionally dependent observations. ERHT contrasts spatial medians on adjacent segments using a ridge-regularized inverse of the pooled centered spatial-sign covariance matrix, thereby combining robustness to radial variation with dependence-aware weighting. We establish Gaussian-process limits for the single- and multiple-change scans and joint convergence over a finite set of regularization parameters. These results provide asymptotically exact calibration of a Cauchy-aggregated adaptive test through the joint Gaussian limit, together with guarantees for local power and single-change localization. We further embed the ERHT score in wild binary segmentation and prove consistency for estimating the number and locations of multiple changes. Simulations show that ERHT is generally well calibrated and delivers competitive power under heavy-tailed distributions, particularly when cross-sectional dependence is substantial. An analysis of the Fama--French 49 industry portfolios reveals persistent evidence of location instability and identifies four structural breaks.

stat.ME↗

arXiv2025

Empirical Likelihood Meets Prediction-Powered Inference

We study inference with a small labeled sample, a large unlabeled sample, and high-quality predictions from an external model. We link prediction-powered inference with empirical likelihood by stacking supervised estimating equations based on labeled outcomes with auxiliary moment conditions built from predictions, and then optimizing empirical likelihood under these joint constraints. The resulting empirical likelihood-based prediction-powered inference (EPI) estimator is asymptotically normal, has asymptotic variance no larger than the fully supervised estimator, and attains the semiparametric efficiency bound when the auxiliary functions span the predictable component of the supervised score. For hypothesis testing and confidence sets, empirical likelihood ratio statistics admit chi-squared-type limiting distributions. As a by-product, the empirical likelihood weights induce a calibrated empirical distribution that integrates supervised and prediction-based information, enabling estimation and uncertainty quantification for general functionals beyond parameters defined by estimating equations. We present two practical implementations: one based on basis expansions in the predictions and covariates, and one that learns an approximately optimal auxiliary function by cross-fitting. In simulations and applications, EPI reduces mean squared error and shortens confidence intervals while maintaining nominal coverage.

stat.ME↗