153 papers
This paper demonstrates that designs minimizing variance under a bias constraint, or minimizing bias under a variance constraint, are equivalent to minimax designs with appropriately tuned constants, and conversely, any minimax design solves these constrained optimization problems for suitable bounds.
This paper introduces composite Lp-quantile regression and near quantile regression as robust, high-efficiency alternatives to existing methods for high-dimensional data with infinite error variance, while also establishing their oracle model selection properties and developing a unified, efficient algorithm for their implementation.
The paper derives a single integral expression valid for all complex numbers that represents the reciprocal gamma function without requiring analytic continuation and simultaneously satisfies a specific functional identity involving the gamma function and sine.
This paper establishes a unified framework using concentration inequalities to analyze the statistical convergence and robustness of depth-based estimators, explicitly deriving their maximum bias curves and breakdown points while demonstrating how slight variations in these inequalities reveal distinct robustness behaviors across different depth formulations.
This paper introduces a distribution-free framework for formalizing identifiability in ill-posed linear regression by defining a constrained least-squares solution and establishing sharp error bounds for statistically interpretable dimensionality reduction algorithms that outperform traditional minimax rates under heavy-tailed features and low effective rank.
This paper introduces a parsimonious Levy-driven graph supOU process for modeling high-dimensional time series with both short- and long-range dependence, develops a consistent generalized method of moments estimator for it, and validates the approach through simulations and an empirical study of European wind capacity factors.
This paper establishes that score-driven updates are uniquely characterized by their ability to reduce the expected Kullback-Leibler divergence relative to the true data-generating density, providing a rigorous information-theoretic foundation that holds even in non-concave, multivariate, and misspecified settings where alternative performance measures fail.
This paper establishes theoretical uniform-in-time error bounds for the deterministic ensemble transform Kalman filter applied to infinite-dimensional nonlinear dynamical systems, demonstrating that appropriate multiplicative covariance inflation ensures bounded estimation errors and justifying its practical effectiveness.
This paper establishes a principled theoretical framework for density aggregation by demonstrating that normalized generalized means with order are the only rules guaranteeing systematic improvements in log-likelihood over individual distributions, thereby providing a unified justification for the widespread use of linear and geometric pooling in Deep Ensembles.
This paper introduces "Bayesian Adversarial Privacy," a new quantitative framework that offers a more contextual and rigorous alternative to differential privacy and statistical disclosure theory by grounding disclosure decisions in a prior viewpoint derived from Bayesian decision theory.
This paper establishes Gaussian approximation bounds for the finite-dimensional distributions of deep neural networks with randomly initialized weights and Lipschitz activations, proving convergence to a Gaussian limit as layer widths grow and deriving specific convergence rates that depend on the network depth.
This paper establishes that low-degree polynomial tests can distinguish between correlated sparse stochastic block models and independent Erdős-Rényi graphs if and only if the subsampling probability exceeds the minimum of Otter's constant and the Kesten-Stigum threshold, thereby identifying a sharp computational transition for detection and partial recovery.
This paper establishes finite-sample convergence guarantees for score-based diffusion models learning intrinsically low-dimensional distributions, demonstrating that their generalization error scales with the data's intrinsic -Wasserstein dimension rather than the ambient dimension, thereby mitigating the curse of dimensionality without requiring restrictive assumptions like compact support or smooth densities.