Related papers: Asymptotics For High Dimensional Regression M-Esti…

This paper discusses asymptotic distributions of various estimators of the underlying parameters in some regression models with long memory (LM) Gaussian design and nonparametric heteroscedastic LM moving average errors. In the simple…

We study asymptotic behavior of one-step weighted $M$-estimators based on samples from arrays of not necessarily identically distributed random variables and representing explicit approximations to the corresponding consistent weighted…

In this paper we study the asymptotics of linear regression in settings with non-Gaussian covariates where the covariates exhibit a linear dependency structure, departing from the standard assumption of independence. We model the covariates…

This paper studies the asymptotics of resampling without replacement in the proportional regime where dimension $p$ and sample size $n$ are of the same order. For a given dataset $(X,y)\in \mathbb{R}^{n\times p}\times \mathbb{R}^n$ and…

This paper explores strong and weak consistency of M-estimators for non-identically distributed data, extending prior work. Emphasis is given to scenarios where data is viewed as a triangular array, which encompasses distributional…

In this work, we consider a multivariate regression model with one-sided errors. We assume for the regression function to lie in a general H\"{o}lder class and estimate it via a nonparametric local polynomial approach that consists of…

This paper studies the estimation and inference for the isotonic regression at the boundary point, an object that is particularly interesting and required in the analysis of monotone regression discontinuity designs. We show that the…

Reduced-rank regression is a dimensionality reduction method with many applications. The asymptotic theory for reduced rank estimators of parameter matrices in multivariate linear models has been studied extensively. In contrast, few…

We study the existence, strong consistency and asymptotic normality of estimators obtained from estimating functions, that are p-dimensional martingale transforms. The problem is motivated by the analysis of evolutionary clustered data,…

We employ stabilization methods and second order Poincar\'e inequalities to establish rates of multivariate normal convergence for a large class of vectors $(H_s^{(1)},...,H_s^{(m)})$, $s \geq 1$, of statistics of marked Poisson processes…

We improve a known result on the strong consistency of M-estimates of the regression parameters in a linear model for independent and identically distributed random errors under some mild conditions.

We propose a general framework for regularization in M-estimation problems under time dependent (absolutely regular-mixing) data which encompasses many of the existing estimators. We derive non-asymptotic concentration bounds for the…

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…

We study asymptotically normal estimation and confidence regions for low-dimensional parameters in high-dimensional sparse models. Our approach is based on the $\ell_1$-penalized M-estimator which is used for construction of a bias…

In this paper we obtain new effective results on the Halpern iterations of nonexpansive mappings using methods from mathematical logic or, more specifically, proof-theoretic techniques. We give effective rates of asymptotic regularity for…

We establish the asymptotic normality of the regression estimator in a fixed-design setting when the errors are given by a field of dependent random variables. The result applies to martingale-difference or strongly mixing random fields. On…

Regularized kernel methods such as, e.g., support vector machines and least-squares support vector regression constitute an important class of standard learning algorithms in machine learning. Theoretical investigations concerning…

We provide a unified analysis of the predictive risk of ridge regression and regularized discriminant analysis in a dense random effects model. We work in a high-dimensional asymptotic regime where $p, n \to \infty$ and $p/n \to \gamma \in…

Most asymptotic results for robust estimates rely on regularity conditions that are difficult to verify in practice. Moreover, these results apply to fixed distribution functions. In the robustness context the distribution of the data…

Let $\alpha_n(\cdot)=P\bigl(X_{n+1}\in\cdot\mid X_1,\ldots,X_n\bigr)$ be the predictive distributions of a sequence $(X_1,X_2,\ldots)$ of $p$-dimensional random vectors. Suppose $$\alpha_n= \mathcal{N} _p (M_n,Q_n)$$ where…