Related papers: Multiscale Asymptotic Normality in Quantile Regres…
Mean-based estimators of causal effects in randomized experiments may behave poorly if the potential outcomes have a heavy tail or contain outliers. An alternative estimator proposed by Rosenbaum (1993) estimates a constant additive…
In general, perturbative expansions of observables in powers of the coupling constant in quantum field theories are asymptotic series. In many cases it is possible to apply resummation techniques to assign a unique finite value to an…
We study average treatment effect (ATE) estimation under complete randomization with many covariates in a design-based, finite-population framework. In randomized experiments, regression adjustment can improve precision of estimators using…
In the standard Gaussian linear measurement model $Y=X\mu_0+\xi \in \mathbb{R}^m$ with a fixed noise level $\sigma>0$, we consider the problem of estimating the unknown signal $\mu_0$ under a convex constraint $\mu_0 \in K$, where $K$ is a…
Frequentists' inference often delivers point estimators associated with confidence intervals or sets for parameters of interest. Constructing the confidence intervals or sets requires understanding the sampling distributions of the point…
The Lasso is a method for high-dimensional regression, which is now commonly used when the number of covariates $p$ is of the same order or larger than the number of observations $n$. Classical asymptotic normality theory does not apply to…
We consider median regression and, more generally, a possibly infinite collection of quantile regressions in high-dimensional sparse models. In these models the overall number of regressors $p$ is very large, possibly larger than the sample…
The paper concerns the $d$-dimensional stochastic approximation recursion, $$ \theta_{n+1}= \theta_n + \alpha_{n + 1} f(\theta_n, \Phi_{n+1}) $$ where $ \{ \Phi_n \}$ is a stochastic process on a general state space, satisfying a…
This paper studies the inference of the regression coefficient matrix under multivariate response linear regressions in the presence of hidden variables. A novel procedure for constructing confidence intervals of entries of the coefficient…
This paper considers estimating functional-coefficient models in panel quantile regression with individual effects, allowing the cross-sectional and temporal dependence for large panel observations. A latent group structure is imposed on…
We address a parametric joint detection-estimation problem for discrete signals of the form $x(t) = \sum_{n=1}^{N} \alpha_n e^{-i \lambda_n t } + \epsilon_t$, $t \in \mathbb{N}$, with an additive noise represented by independent centered…
The main Theorem of Jain et al.[Jain, K., Singh, S., and Sharma, S. (2011), Re- stricted estimation in multivariate measurement error regression model; JMVA, 102, 2, 264-280] is established in its full generality. Namely, we derive the…
Analysis of non-asymptotic estimation error and structured statistical recovery based on norm regularized regression, such as Lasso, needs to consider four aspects: the norm, the loss function, the design matrix, and the noise model. This…
Large Language Models (LLMs) have demonstrated remarkable capabilities, yet their scalability raises a critical question: Have we reached the scaling ceiling? This paper addresses this pivotal question by developing a unified theoretical…
Sample covariance matrices are widely used in multivariate statistical analysis. The central limit theorems (CLT's) for linear spectral statistics of high-dimensional non-centered sample covariance matrices have received considerable…
Quantile regression is a powerful tool for learning the relationship between a response variable and a multivariate predictor while exploring heterogeneous effects. In this paper, we consider statistical inference for quantile regression…
This article carries out a large dimensional analysis of standard regularized discriminant analysis classifiers designed on the assumption that data arise from a Gaussian mixture model with different means and covariances. The analysis…
We establish the asymptotic normality of the kernel type estimator for the regression function constructed from quasi-associated data when the explanatory variable takes its values in a separable Hilbert space.
High-dimensional linear regression under heavy-tailed noise or outlier corruption is challenging, both computationally and statistically. Convex approaches have been proven statistically optimal but suffer from high computational costs,…
Many scientific problems involve data exhibiting both temporal and cross-sectional dependencies. While linear dependencies have been extensively studied, the theoretical analysis of regression estimators under nonlinear dependencies remains…