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Variance estimation in the linear model when $p > n$ is a difficult problem. Standard least squares estimation techniques do not apply. Several variance estimators have been proposed in the literature, all with accompanying asymptotic…
In this paper, we establish universal approximation theorems for neural networks applied to general nonlinear ill-posed operator equations. In addition to the approximation error, the measurement error is also taken into account in our…
Method of moment estimators exhibit appealing statistical properties, such as asymptotic unbiasedness, for nonconvex problems. However, they typically require a large number of samples and are extremely sensitive to model misspecification.…
Parameter estimation in a class of heteroscedastic time series models is investigated. The existence of conditional least-squares and conditional likelihood estimators is proved. Their consistency and their asymptotic normality are…
We consider the problem of parameter estimation in a high-dimensional generalized linear model. Spectral methods obtained via the principal eigenvector of a suitable data-dependent matrix provide a simple yet surprisingly effective…
Unsupervised and self-supervised learning approaches have become a crucial tool to learn representations for downstream prediction tasks. While these approaches are widely used in practice and achieve impressive empirical gains, their…
We consider the problem of asymptotic reconstruction of the state and parameter values in systems of ordinary differential equations. A solution to this problem is proposed for a class of systems of which the unknowns are allowed to be…
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 practice it is often found that large over-parameterized neural networks generalize better than their smaller counterparts, an observation that appears to conflict with classical notions of function complexity, which typically favor…
We consider a linear mixed-effects model with a clustered structure, where the parameters are estimated using maximum likelihood (ML) based on possibly unbalanced data. Inference with this model is typically done based on asymptotic theory,…
This paper is motivated by an open problem around deep networks, namely, the apparent absence of over-fitting despite large over-parametrization which allows perfect fitting of the training data. In this paper, we analyze this phenomenon in…
The combination of deep neural nets and theory-driven models, which we call deep grey-box modeling, can be inherently interpretable to some extent thanks to the theory backbone. Deep grey-box models are usually learned with a regularized…
Despite their outstanding performance, large language models (LLMs) suffer notorious flaws related to their preference for simple, surface-level textual relations over full semantic complexity of the problem. This proposal investigates a…
Most of the recent results in polynomial functional regression have been focused on an in-depth exploration of single-parameter regularization schemes. In contrast, in this study we go beyond that framework by introducing an algorithm for…
This work considers the problem of binary classification: given training data $x_1, \dots, x_n$ from a certain population, together with associated labels $y_1,\dots, y_n \in \left\{0,1 \right\}$, determine the best label for an element $x$…
This paper studies the properties of debiased machine learning (DML) estimators under a novel asymptotic framework, offering insights for improving the performance of these estimators in applications. DML is an estimation method suited to…
Functional data present as functions or curves possessing a spatial or temporal component. These components by nature have a fixed observational domain. Consequently, any asymptotic investigation requires modelling the increased correlation…
We tackle the problem of building adaptive estimation procedures for ill-posed inverse problems. For general regularization methods depending on tuning parameters, we construct a penalized method that selects the optimal smoothing sequence…
Unbiased estimators are introduced for averaged Bregman divergences which generalize Stein's Unbiased (Predictive) Risk Estimator, and the minimization of these estimators is proposed as a regularization parameter selection method for…
Sequential data collection has emerged as a widely adopted technique for enhancing the efficiency of data gathering processes. Despite its advantages, such data collection mechanism often introduces complexities to the statistical inference…