Related papers: Universality in block dependent linear models with…
The generalized linear model is widely used in all areas of applied statistics and while correct asymptotic inference can be achieved under misspecification of the distributional assumptions, a correctly specified mean structure is crucial…
We introduce a sufficient graphical model by applying the recently developed nonlinear sufficient dimension reduction techniques to the evaluation of conditional independence. The graphical model is nonparametric in nature, as it does not…
Since the pioneering work of Gerhard Gruss dating back to 1935, Gruss's inequality and, more generally, Gruss-type bounds for covariances have fascinated researchers and found numerous applications in areas such as economics, insurance,…
Nonlinear causal discovery from observational data imposes strict identifiability assumptions on the formulation of structural equations utilized in the data generating process. The evaluation of structure learning methods under assumption…
Consider the case that we observe $n$ independent and identically distributed copies of a random variable with a probability distribution known to be an element of a specified statistical model. We are interested in estimating an infinite…
In this paper, we study the issue of estimating a structured signal $x_0 \in \mathbb{R}^n$ from non-linear and noisy Gaussian observations. Supposing that $x_0$ is contained in a certain convex subset $K \subset \mathbb{R}^n$, we prove that…
Structural independence is the (conditional) independence that arises from the structure rather than the precise numerical values of a distribution. We develop this concept and relate it to $d$-separation and structural causal models.…
We study the coverage properties of full conformal regression in the proportional asymptotic regime where the ratio of the dimension and the sample size converges to a constant. In this setting, existing theory tells us only that full…
We characterize the squared prediction risk of ensemble estimators obtained through subagging (subsample bootstrap aggregating) regularized M-estimators and construct a consistent estimator for the risk. Specifically, we consider a…
Most modern learning problems are over-parameterized, where the number of learnable parameters is much greater than the number of training data points. In this over-parameterized regime, the training loss typically has infinitely many…
We derive a scale-free bound on the density of the maximum of a centered Gaussian vector. The basic bound is non-uniform, depends logarithmically on the dimension, and allows any covariance matrix. When the largest marginal variance is…
We consider a finite impulse response system with centered independent sub-Gaussian design covariates and noise components that are not necessarily identically distributed. We derive non-asymptotic near-optimal estimation and prediction…
We describe a design-based framework for drawing causal inference in general randomized experiments. Causal effects are defined as linear functionals evaluated at unit-level potential outcome functions. Assumptions about the potential…
In this paper, we consider the nonparametric regression problem with multivariate predictors. We provide a characterization of the degrees of freedom and divergence for estimators of the unknown regression function, which are obtained as…
Recently, Hammond and Sheffield introduced a model of correlated random walks that scale to fractional Brownian motions with long-range dependence. In this paper, we consider a natural generalization of this model to dimension $d\geq 2$. We…
We develop a design-based framework for causal inference that accommodates random potential outcomes without introducing outcome models, thereby extending the classical Neyman--Rubin paradigm in which outcomes are treated as fixed. By…
We present a method for drawing isolines indicating regions of equal joint exceedance probability for bivariate data. The method relies on bivariate regular variation, a dependence framework widely used for extremes. This framework enables…
The paper considers so-called adaptive estimations of regression, distribution density and spectral density of a Gaussian stationary sequence, asymptotically optimal in order at a growing number of observation on any regular subspace…
A block covariance structure is widely observed across large-scale and high-dimensional datasets in diverse fields such as biology, medicine, engineering, economics, and finance. This pattern entails partitioning a covariance matrix into…
Genetic prediction of complex traits and diseases has attracted enormous attention in precision medicine, mainly because it has the potential to translate discoveries from genome-wide association studies (GWAS) into medical advances. As the…