146 papers
This paper provides axiomatic characterizations of generalized and standard -estimators by establishing that symmetry, (strong) internality, and asymptotic idempotency are the defining properties, utilizing a separation theorem for Abelian subsemigroups in the proofs.
This paper proposes a hierarchical Bayesian dynamic game framework for competitive inventory and pricing under incomplete information, integrating Bayesian learning, strategic belief updating, and a credible-risk criterion to derive a conservative equilibrium that effectively balances profit maximization with uncertainty management.
This paper establishes sharp nonasymptotic oracle inequalities and minimax optimal convergence rates for sparse Lasso and Slope estimators of high-dimensional drift matrices in Lévy-driven Ornstein--Uhlenbeck processes based on discrete observations, thereby extending high-dimensional statistical theory to systems driven by pure jump noise.
This paper establishes the consistency and asymptotic normality of the Whittle estimator for Lévy-driven CARMA models observed at renewal times, demonstrating that the integrated periodogram-based approach remains robust under mild conditions even when the driving noise exhibits heavy tails and jumps.
This paper establishes a minimax theory for nonparametric regression under covariate shift by introducing a transfer function to characterize convergence rates that range from classical benchmarks to accelerated regimes involving multiplicative sample size interactions, all achievable by a design-adaptive estimator even with unbounded covariate support.
This paper establishes a geometric framework using principal fiber bundles to identify fundamental obstructions in learning differential equations from temporal Random Dot Product Graphs, characterizing the interplay between gauge ambiguity, spectral gaps, and holonomy while demonstrating that symmetric dynamics can resolve gauge issues to enable vector field recovery.
This paper proposes "Artificial Replay," a new experimental design that reuses recorded rewards from a single policy trajectory to enable unbiased, cost-effective, and low-variance comparisons between multi-armed bandit algorithms, thereby significantly reducing the number of required user interactions compared to traditional independent restarts.
This paper introduces a partition-based functional ridge regression framework that decomposes coefficient functions into dominant and weaker components to apply differential penalization, thereby improving numerical stability, interpretability, and predictive performance in high-dimensional functional linear models without relying on explicit variable selection.
This paper proposes a novel, computationally efficient estimator for polychoric correlation that minimizes a robust loss function to withstand partial model misspecification—such as careless responding—without requiring assumptions about the nature or extent of the errors, thereby offering a more reliable alternative to traditional maximum likelihood estimation in rating data analysis.
This paper establishes a central limit theorem for large network formation models with strategic interactions and homophily by adapting stabilization conditions from geometric graphs and deriving interpretable primitive conditions based on branching process theory to justify practical inference procedures.
This paper demonstrates that a noncentral Wishart mixture of noncentral Wishart distributions with identical degrees of freedom remains a noncentral Wishart distribution, a result used to derive the finite-sample distribution for testing random effects in two-factor and general factorial design models with multivariate normal data.
This paper establishes a unified thermodynamic response framework for singular Bayesian models, demonstrating that posterior tempering induces a hierarchy of observables that naturally interpret complex learning-theoretic quantities like the real log canonical threshold and WAIC as free-energy derivatives, thereby revealing phase-transition-like structural reorganizations in models such as neural networks and Gaussian mixtures.
This paper establishes a comprehensive statistical theory for globally optimal empirical risk minimization decision trees by deriving sharp oracle inequalities and minimax optimal rates over a novel piecewise sparse heterogeneous anisotropic Besov space, thereby providing rigorous theoretical guarantees for their performance in high-dimensional regression and classification under both sub-Gaussian and heavy-tailed noise settings.
This paper demonstrates that predictive inference is governed by four distinct, pairwise non-nested admissibility geometries—Blackwell risk dominance, anytime-valid supermartingales, marginal coverage, and Cesàro approachability—each offering a unique certificate of optimality and proving that admissibility is irreducibly relative to the chosen criterion rather than a universal property.
This paper investigates the extreme values of sparse, equicorrelated Gaussian fields on a triangular grid to identify the correlation threshold where the standard Gumbel law fails, utilizing the Chen-Stein method to resolve open questions in high-dimensional statistics and multiple testing.
This paper establishes novel and strictly sharper Berry-Esseen bounds for the second moment estimator of asymptotically stationary Gaussian processes observed at high frequency, specifically deriving convergence rates in total variation, Kolmogorov, and Wasserstein distances for the drift parameters of Gaussian Ornstein-Uhlenbeck processes.
This paper proposes a robust parametric framework based on the minimum density power divergence estimator (MDPDE) that achieves asymptotically consistent jump detection in high-frequency CIR and CKLS models by exploiting the scale separation between diffusion and jump increments to establish a Gumbel-distributed detection threshold.
This paper proposes a robust estimation method for diffusion processes using -divergence to mitigate the impact of outliers in high-frequency data, establishing its asymptotic properties and bounded influence functions through Gaussian approximation of transition densities.
This paper establishes the strong consistency and convergence rates of a local linear estimator for generalized regression with dependent functional data, demonstrating its superior performance over the local constant estimator through both theoretical analysis and empirical applications in energy forecasting.
This paper introduces an augmented van Trees inequality that provides uniformly tighter lower bounds on minimax squared Bayes risk than the classical version, accommodates priors with non-vanishing boundary densities, and enables the derivation of sharper or exact minimax constants for various nonparametric estimation problems, including high-dimensional regression.