Related papers: Local bilinear multiple-output quantile/depth regr…
It is well known that aspects of the formation of localised states in a one-dimensional Swift--Hohenberg equation can be described by Ginzburg--Landau-type envelope equations. This paper extends these multiple scales analyses to cases where…
We introduce a technique to automatically convert local boundary conditions into nonlocal volume constraints for nonlocal Poisson's and peridynamic models. The proposed strategy is based on the approximation of nonlocal Dirichlet or Neumann…
Clustered sampling is prevalent in empirical regression discontinuity (RD) designs, but it has not received much attention in the theoretical literature. In this paper, we introduce a general model-based framework for such settings and…
Linear regression studies the problem of estimating a model parameter $\beta^* \in \mathbb{R}^p$, from $n$ observations $\{(y_i,\mathbf{x}_i)\}_{i=1}^n$ from linear model $y_i = \langle \mathbf{x}_i,\beta^* \rangle + \epsilon_i$. We…
We consider the bilinear inverse problem of recovering two vectors, $\boldsymbol{x} \in\mathbb{R}^L$ and $\boldsymbol{w} \in\mathbb{R}^L$, from their entrywise product. We consider the case where $\boldsymbol{x}$ and $\boldsymbol{w}$ have…
This study extends the Bayesian nonparametric instrumental variable regression model to determine the structural effects of covariates on the conditional quantile of the response variable. The error distribution is nonparametrically…
We consider a class of nonlocal viscous Cahn-Hilliard equations with Neumann boundary conditions for the chemical potential. The double-well potential is allowed to be singular (e.g. of logarithmic type), while the singularity of the…
Due to unmeasured confounding, it is often not possible to identify causal effects from a postulated model. Nevertheless, we can ask for partial identification, which usually boils down to finding upper and lower bounds of a causal quantity…
Quantile regression (QR) is becoming increasingly popular due to its relevance in many scientific investigations. However, application of QR can become very challenging when dealing with high-dimensional data, making it necessary to use…
Many applications of LLM-based text regression require predicting a full conditional distribution rather than a single point value. We study distributional regression under empirical-quantile supervision, where each input is paired with…
A class of simultaneous equation models arise in the many domains where observed binary outcomes are themselves a consequence of the existing choices of of one of the agents in the model. These models are gaining increasing interest in the…
This paper considers (partial) identification of a variety of counterfactual parameters in binary response models with possibly endogenous regressors. Our framework allows for nonseparable index functions with multi-dimensional latent…
We complete our boundedness theory of commutators of bilinear bi-parameter singular integrals by establishing the following result. If $T$ is a bilinear bi-parameter singular integral satisfying suitable $T1$ type assumptions,…
Spatial orientation is a fundamental cognitive skill that relies on sensory information to update perceived direction. Understanding how sensory conditions influence directional accuracy is important for both cognitive science and the…
Multiple kernel methods less consider the intrinsic manifold structure of multiple kernel data and estimate the consensus kernel matrix with quadratic number of variables, which makes it vulnerable to the noise and outliers within multiple…
We study local asymptotic normality of M-estimates of convex minimization in an infinite dimensional parameter space. The objective function of M-estimates is not necessary differentiable and is possibly subject to convex constraints. In…
When building a geometric scene understanding system for autonomous vehicles, it is crucial to know when the system might fail. Most contemporary approaches cast the problem as depth regression, whose output is a depth value for each pixel.…
We present a structured additive regression approach to model conditional densities given scalar covariates, where only samples of the conditional distributions are observed. This links our approach to distributional regression models for…
It is a challenge to manage infinite- or high-dimensional data in situations where storage, transmission, or computation resources are constrained. In the simplest scenario when the data consists of a noisy infinite-dimensional signal, we…
We present in a unified setting the foundations for a theory of non-bilinear Dirichlet functionals on Hilbert spaces. We prove known and new equivalences between non-linear semigroups, non-linear resolvents, non-linear generators, and their…