Related papers: Tuning-free one-bit covariance estimation using da…
We consider applying stochastic approximation (SA) methods to solve nonsmooth variational inclusion problems. Existing studies have shown that the averaged iterates of SA methods exhibit asymptotic normality, with an optimal limiting…
We study online inference and asymptotic covariance estimation for the stochastic gradient descent (SGD) algorithm. While classical methods (such as plug-in and batch-means estimators) are available, they either require inaccessible…
Given a sample of i.i.d. high-dimensional centered random vectors, we consider a problem of estimation of their covariance matrix $\Sigma$ with an additional assumption that $\Sigma$ can be represented as a sum of a few Kronecker products…
We study inference for censored survival data where some covariates are distorted by some unknown functions of an observable confounding variable in a multiplicative form. Example of this kind of data in medical studies is the common…
We consider nonparametric estimation of a covariance function on the unit square, given a sample of discretely observed fragments of functional data. When each sample path is only observed on a subinterval of length $\delta<1$, one has no…
In this paper, we study the problem of high-dimensional approximately low-rank covariance matrix estimation with missing observations. We propose a simple procedure computationally tractable in high-dimension and that does not require…
This paper considers the problem of design-based inference for the average treatment effect in finely stratified experiments. Here, by "design-based'' we mean that the only source of uncertainty stems from the randomness in treatment…
Analysis of high-dimensional data, where the number of covariates is larger than the sample size, is a topic of current interest. In such settings, an important goal is to estimate the signal level $\tau^2$ and noise level $\sigma^2$, i.e.,…
We obtain robust and computationally efficient estimators for learning several linear models that achieve statistically optimal convergence rate under minimal distributional assumptions. Concretely, we assume our data is drawn from a…
This work is concerned with the estimation of multidimensional regression and the asymptotic behaviour of the test involved in selecting models. The main problem with such models is that we need to know the covariance matrix of the noise to…
Unrolled deep neural networks have attracted significant attention for their success in various practical applications. In this paper, we explore an application of deep unrolling in the direction of arrival (DoA) estimation problem when…
We propose a new estimator for the high-dimensional linear regression model with observation error in the design where the number of coefficients is potentially larger than the sample size. The main novelty of our procedure is that the…
Assume that $X_{1}, \ldots, X_{N}$ is an $\varepsilon$-contaminated sample of $N$ independent Gaussian vectors in $\mathbb{R}^d$ with mean $\mu$ and covariance $\Sigma$. In the strong $\varepsilon$-contamination model we assume that the…
Local polynomial regression of order at least one often performs poorly in regions of sparse data. Local constant regression is exceptional in this regard, though it is the least accurate method in general, especially at the boundaries of…
We address the inference problem concerning regression coefficients in a classical linear regression model using least squares estimates. The analysis is conducted under circumstances where network dependency exists across units in the…
We propose a new pivotal method for estimating high-dimensional matrices. Assume that we observe a small set of entries or linear combinations of entries of an unknown matrix $A\_0$ corrupted by noise. We propose a new method for estimating…
The minimum covariance determinant (MCD) estimator is ubiquitous in multivariate analysis, the critical step of which is to select a subset of a given size with the lowest sample covariance determinant. The concentration step (C-step) is a…
This paper addresses the problem of inverse covariance (also known as precision matrix) estimation in high-dimensional settings. Specifically, we focus on two classes of estimators: linear shrinkage estimators with a target proportional to…
When data are clustered, common practice has become to do OLS and use an estimator of the covariance matrix of the OLS estimator that comes close to unbiasedness. In this paper we derive an estimator that is unbiased when the random-effects…
Performing statistical inference in high-dimension is an outstanding challenge. A major source of difficulty is the absence of precise information on the distribution of high-dimensional estimators. Here, we consider linear regression in…