143 papers
This paper extends the definition of the multidimensional Dickman distribution to vector-valued random elements characterized as fixed points of a specific affine transformation, proving their infinite divisibility and operator selfdecomposability while identifying cases where they emerge as limiting distributions.
This paper provides a comprehensive statistical analysis of the "Einstein from noise" phenomenon, demonstrating how template bias causes pure noise observations to converge to the template's structural features in both Fourier phases and magnitudes, thereby revealing critical pitfalls in template matching techniques across multiple scientific disciplines.
This paper introduces a general framework for "central subspace data depths," a new class of statistical tools that order multivariate data from a central subspace rather than a single point, thereby extending symmetry-based analysis to higher-dimensional structures and demonstrating practical utility in fraud detection.
This paper presents a vector generalization of the curvature-corrected Cramér-Rao bound for multivariate parameters in the nonasymptotic regime, utilizing extrinsic geometry and sum-of-squares relaxations to derive directional and matrix-valued refinements that offer more faithful estimation limits than classical second-order corrections, as demonstrated through curved Gaussian and spherical multinomial models.
This paper presents a geometric refinement of the classical Cramér-Rao bound in the non-asymptotic regime by leveraging the extrinsic curvature of the statistical model manifold's square root embedding to derive tighter, curvature-aware lower bounds on estimator variance.
This paper characterizes the Palm distributions of superposed independent point processes through a mixture representation, enabling new statistical inference strategies for minimum contrast estimation of corrupted processes and likelihood-based analysis of shot noise Cox processes.
This paper presents an efficient method for sketching stochastic valuation functions by constructing discretized item value distributions with logarithmic support size that provide constant-factor approximations for monotone subadditive or submodular functions, thereby enabling scalable solutions for complex optimization problems like welfare maximization.
This paper establishes uniform Lorden-type moment bounds for the overshoot of random walks with sign-changing increments from standard exponential families in the small-drift regime, demonstrating that these bounds improve to a constant of 1 for large barriers and providing explicit exponential convergence rates interpreted through optimal transport metrics.
This paper determines the exact attainable region between Chatterjee's rank correlation and Blest's rank correlation over all bivariate copulas by solving a constrained optimization problem via Karush–Kuhn–Tucker conditions, which yields a novel extremal copula family providing closed-form expressions that explicitly parametrize the boundary of the region.
This paper establishes the limit distributions for the last occurrence and total count of times a strongly consistent estimator deviates from its target by at least as , providing a unified framework applicable to parametric and nonparametric settings that yields new optimality results for maximum likelihood estimators and methods for constructing sequential confidence sets.
This paper investigates the statistical limits of detecting multiple inhomogeneous submatrices within a large Gaussian random matrix under both arbitrary and consecutive index placement regimes, establishing information-theoretic lower bounds and proposing matching algorithms for mean-shift and variance-shift signal models.
This paper investigates second-order asymptotics for the number of times a strongly consistent estimator deviates from its target by more than , introducing a concept of "asymptotic relative deficiency" to distinguish between estimators with identical first-order efficiency and demonstrating that specific finite-sample corrections (such as using for normal variance) minimize the expected number of such errors.
This paper introduces a convex optimization framework for univariate nonparametric shape-constrained density estimation using -Wasserstein projection, specifically analyzing non-increasing and log-concave densities to establish their structural properties, propose a discretized implementation, and compare their performance against maximum likelihood estimators.
This paper introduces a filtration-based sequential learning framework that decomposes the impact of adding taxa on phylodynamic inference into learning, mismatch, and covariance components, revealing fundamental limits on what sequence data alone can reveal about latent genealogies due to irreducible gaps between analyst and oracle performance.
This paper establishes a geometric framework demonstrating that the leading-order bias of posterior functionals in variational inference is determined by the component of the functional orthogonal to the variational tangent space, thereby explaining why structured mean-field approximations systematically distort cross-block dependencies due to omitted interaction directions.
This paper proposes a robust, data-driven framework for assortment optimization that maximizes worst-case expected revenue under potential customer preference shifts, establishing computational tractability and deriving statistically optimal algorithms with tight sample complexity bounds to ensure reliable generalization.
This paper introduces Adaptive Importance Sampling and Stratified Subsampling estimators that achieve minimax-optimal rates for robust high-dimensional sparse regression under heavy-tailed noise, contamination, and temporal dependence, while also providing fully specified de-biasing procedures for valid confidence intervals and demonstrating superior empirical performance over uniform subsampling.
This paper introduces ULFS-KDPE, a novel kernel-based estimator that achieves semiparametric efficiency for pathwise differentiable parameters in nonparametric models by constructing a data-adaptive debiasing flow via a universal least favorable submodel, thereby eliminating the need for explicit efficient influence function derivation while ensuring rigorous theoretical guarantees and computational tractability.
This paper establishes a non-standard analysis framework that unifies coherent risk measures and their finite-sample estimators through hyperfinite representations, yielding discrete Kusuoka formulae, plug-in consistency results, and asymptotic normality via a transparent probability-to-statistics dictionary.
This paper develops Generalized Method of Moments (GMM) and M estimators for network-dependent data by establishing a novel uniform law of large numbers that ensures their consistency and asymptotic normality, while also providing complete procedures for practical estimation and inference.