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Debiased machine learning (DML) offers an attractive way to estimate treatment effects in observational settings, where identification of causal parameters requires a conditional independence or unconfoundedness assumption, since it allows…
In this paper, we obtain the central limit theorems for LS estimator in simple linear errors-in-variables (EV) regression models under some mild conditions. And we also show that those conditions are necessary in some sense.
The panel data regression models have gained increasing attention in different areas of research including but not limited to econometrics, environmental sciences, epidemiology, behavioral and social sciences. However, the presence of…
The generalization ability of minimizers of the empirical risk in the context of binary classification has been investigated under a wide variety of complexity assumptions for the collection of classifiers over which optimization is…
In the present paper we investigate the predictive risk of possibly misspecified quantile regression functions. The in-sample risk is well-known to be an overly optimistic estimate of the predictive risk and we provide two relatively simple…
In this paper, we consider the usual linear regression model in the case where the error process is assumed strictly stationary. We use a result from Hannan (1973), who proved a Central Limit Theorem for the usual least square estimator…
This article describes a multivariate polynomial regression method where the uncertainty of the input parameters are approximated with Gaussian distributions, derived from the central limit theorem for large weighted sums, directly from the…
We propose a new method of estimation in high-dimensional linear regression model. It allows for very weak distributional assumptions including heteroscedasticity, and does not require the knowledge of the variance of random errors. The…
This paper proposes a quasi-maximum likelihood (QML) estimator for break points in high-dimensional factor models, specifically accounting for multiple structural breaks. We begin by establishing a necessary and sufficient condition to…
Recent research has focused on $\ell_1$ penalized least squares (Lasso) estimators for high-dimensional linear regressions in which the number of covariates $p$ is considerably larger than the sample size $n$. However, few studies have…
We study the optimal linear prediction of a random function that takes values in an infinite dimensional Hilbert space. We begin by characterizing the mean square prediction error (MSPE) associated with a linear predictor and discussing the…
We introduce a general mathematical framework for distributed algorithms, and a monotonicity property frequently satisfied in application. These properties are leveraged to provide finite-time guarantees for converging algorithms, suited…
Measuring geometric similarity between high-dimensional network representations is a topic of longstanding interest to neuroscience and deep learning. Although many methods have been proposed, only a few works have rigorously analyzed their…
We study the problem of high-dimensional linear regression in a robust model where an $\epsilon$-fraction of the samples can be adversarially corrupted. We focus on the fundamental setting where the covariates of the uncorrupted samples are…
This paper studies high-dimensional M-estimation in the proportional asymptotic regime (p/n -> gamma > 0) when the noise distribution has infinite variance. For noise with regularly-varying tails of index alpha in (1,2), we establish that…
In this article, we derive the weak limiting distribution of the least squares estimator (LSE) of a convex probability mass function (pmf) with a finite support. We show that it can be defined via a certain convex projection of a Gaussian…
Recently, direct data-driven prediction has found important applications for controlling unknown systems, particularly in predictive control. Such an approach provides exact prediction using behavioral system theory when noise-free data are…
Despite a large and significant body of recent work focused on estimating the out-of-sample risk of regularized models in the high dimensional regime, a theoretical understanding of this problem for non-differentiable penalties such as…
The small sample universal hypothesis testing problem is investigated in this paper, in which the number of samples $n$ is smaller than the number of possible outcomes $m$. The goal of this work is to find an appropriate criterion to…
This paper provides a unified framework for analyzing tensor estimation problems that allow for nonlinear observations, heteroskedastic noise, and covariate information. We study a general class of high-dimensional models where each…