Statistics Theory (Mathematics) Papers of the Week

We focus on a rare feature diversity model, in which most features are useless, but a small fraction promote discrimination among classes in a way that can be detected by a per-feature diversity test, such as one-way ANOVA or the Kruskal-Wallis test. For this setting, we propose Diversity Pursuit Higher Criticism Thresholding (DP-HCT), a feature-screening procedure that applies a higher-criticism threshold to the collection of p-values obtained from per-feature diversity tests.

This paper presents a near-quadratic-time algorithm that correctly matches almost all nodes of two correlated Erdős-Rényi graphs without any incorrect matches.

We discuss methods for estimating triangular maps from finite samples, as well as their use in simulation-based inference and causal inference.

We study the fundamental limits of jointly estimating the signal amplitude and the atmospheric phase distortion in complex-valued multi-look coherent imaging, where the measurements are corrupted by multiplicative speckle and additive Gaussian noise, all looks share a known Gaussian sensing matrix, and both parameters belong to structured classes.

Marginal permutation is exact for testing marginal independence but generally invalid for conditional independence because it breaks the dependence between the exposure ($\bm X$) and covariates ($\bm Z$). In this paper, we show that empirical studentization can nevertheless make this deliberately misspecified resampling scheme asymptotically valid for important conditional independence tests based on scores.

We study natural exponential families whose generalized variance, the determinant of the covariance matrix, is log-affine in the natural parameter.

We study the empirical degree distribution of sparse $L^p$ graphon models, allowing unbounded kernels and hence heavy-tailed degrees.

Large fits often use an adaptive optimizer, such as adaptive moment estimation (Adam), with fixed averaging rates. We show that these rates can change what is estimated, not just how fast: the same observations drive the updates and the optimizer's step-size scaling, moving the fit away from the intended TD value.

Consider the classical statistical problem of sub-Gaussian mean estimation under martingale dependence: given $n$ observations with conditional mean $\mu$ and a known conditional sub-Gaussian proxy $s>0$, we seek a nonasymptotically valid confidence interval for $\mu$.

Combining it with direct information-theoretic arguments, such as testing-to-estimation reductions, we obtain old and new functional inequalities: - For the Poincaré inequality, corresponding to $\Phi(x)=(x-1)^2$, we give a simple static information-theoretic proof that the Poincaré constant of an isotropic log-concave measure on $\mathbb{R}^n$ is $O(n^{1/2})$, first proven via stochastic localization in the seminal work of Lee and Vempala.

In this paper, we develop a projected instrumental variable framework that relaxes conventional assumptions for causal identification with instrumental variables.

In this paper, we develop design-based inference for the distribution of ITEs whose validity relies solely on the randomization of treatment assignment, treating the potential outcomes as arbitrary fixed constants.

We study the query complexity of sampling from smooth distributions on $\mathbb R^d$ using first-order oracles.

We construct counterexamples using three planar observations, a density with full triangular support, and positive-definite matrix data admitting an indefinite optimal representative under the Frobenius norm.

We develop a computation that maintains lower and upper bounds on the ideal endpoint for a prescribed ordering.

In this paper, we study the regularization approach over Sobolev balls under $L^2$-separation, which reveals the connection between the two approaches.

This paper develops feasible high-frequency inference for the leverage effect when the spot variance follows rough Volterra dynamics, leverage loadings depend on endogenous rough states, and observed prices may be contaminated by microstructure noise.

We study the power of the generalized edge-count test on a directed 1-nearest-neighbor graph.

We study the gradient query complexity of sampling from a density $\pi(x)\propto\mathrm{e}^{-V(x)}$ on $\mathbb{R}^d$, where $V$ has a $\beta$-Lipschitz gradient but need not be convex.