153 papers
This paper introduces a fully automatic, fully Bayesian method for constructing irregular histograms that simultaneously selects the optimal number and location of bins, demonstrating consistency and minimax convergence rates while performing competitively with existing procedures in simulations.
This paper derives explicit total variation error bounds for approximating the number of maxima and near-maxima in independent samples using logarithmic, Poisson, and negative binomial distributions, supported by new applications of Stein's method and illustrated through geometric, Gumbel, and uniform examples.
This paper proposes two-stage sequential estimators for relative risk, odds ratio, and their logarithms that guarantee a target mean-square error for any population parameters while maintaining a controlled sample size ratio and achieving high efficiency near the Cramér-Rao bound.
This paper introduces an optimal uniform mean estimator that, by combining Talagrand's generic chaining with single-variable mean estimation, achieves a near-optimal error bound for classes of mean-zero functions under minimal assumptions, thereby resolving key challenges in high-dimensional probability and statistics.
This paper establishes the minimax rates for robust mean estimation under star-shaped constraints in the presence of adversarial corruption and Gaussian or sub-Gaussian noise, characterizing the optimal error bounds in terms of the local entropy of the constraint set, the noise variance, and the corruption fraction.
This paper establishes the minimax rate optimality of three popular matrix completion estimators by leveraging advanced matrix concentration inequalities to eliminate the dimensional factor in their convergence rates.
This paper characterizes the necessary and sufficient conditions for the least squares estimator to be minimax optimal in a convex constrained Gaussian sequence model by linking optimality to the Lipschitz property of the local Gaussian width, while providing algorithms to compute worst-case risk and demonstrating these results across various geometric sets.
This paper proposes and analyzes a simultaneous M-estimator for detecting a change point and recovering diffusivity values in a stochastic heat equation with space-dependent diffusivity, demonstrating that the change point converges at rate while diffusivity constants converge at rate based on local spatial measurements.
This paper establishes convergence rates for scalable pseudo-likelihood-based -estimators of random graph models with dependent edges and increasing parameter dimensions, addressing challenges like phase transitions and near-degeneracy through a novel class of generalized -models.
This paper provides a general characterization of the class of sine-skewed models on the d-dimensional torus that exhibit a singular Fisher information matrix near symmetry, thereby resolving an open question regarding the conditions under which this inferential issue occurs.
This paper establishes a strengthened comparison theorem for the extreme eigenvalues of sums of independent random symmetric matrices against Gaussian counterparts, leveraging this result to improve eigenvalue bounds across various fields and providing the first complete proof of the injectivity properties for sparse random dimension reduction maps conjectured by Nelson & Nguyen.
This paper establishes new extremal properties for geometric quantiles under minimal assumptions, deriving moment-free bounds on their norms and revealing a novel connection between their lower bounds and Tukey depth central regions.
This paper proposes a model-free spectral inference method based on eigengap ratios that effectively determines the number of communities in both dense and sparse networks with a diverging number of communities, without requiring explicit model fitting or parameter tuning.
The paper introduces the Pivotal Information Criterion (PIC), a continuous optimization method that dynamically selects its penalty parameter at the detection boundary to overcome the high false discovery rates and computational infeasibility of traditional criteria like BIC and AIC in high-dimensional settings.
This paper establishes the relationship between the generalized circular projected Cauchy distribution and the wrapped Cauchy distribution, proposes a log-likelihood ratio test for comparing two angular means without assuming equal concentration parameters, and evaluates the test's performance through simulations when the underlying distribution is incorrectly assumed to be wrapped Cauchy.
This paper generalizes a previous result on outlier eigenvectors by establishing that for sparse non-Hermitian random matrices with finite-rank perturbations, the squared projection of an outlier eigenvector onto the spike eigenspace converges in probability to $1-|\mu|^{-2}$, thereby solving Open Problem 5.
This paper investigates the projected isotropic normal distribution, deriving new properties and practical approximations for its mean resultant statistic to facilitate phase-based analysis of EEG signals recorded during flash stimulation.
This paper demonstrates that kernel smoothed estimators for multi-index models equipped with large bandwidth matrix elements naturally overcome the curse of dimensionality by achieving optimal convergence rates determined by the effective dimension rather than the total number of variables, even without explicitly eliminating irrelevant predictors.
This paper completes Le Cam's program by establishing a necessary and sufficient condition for the existence of nontrivial hypothesis tests between two sets of probability measures without requiring a common dominating measure, specifically by utilizing the closures of their convex hulls within the space of bounded finitely additive measures.
This paper establishes a universal, asymptotically optimal concentration bound for sums of arbitrarily dependent random variables by leveraging the subadditivity of expected shortfall and constructing explicit extremal couplings, while providing practical conditions for deriving simple tail profiles based on convex transformation order comparisons.