Related papers: Uniform estimates for the Penalized Boundary Obsta…

We develop a continuous-time penalized regression framework for the estimation of time-varying coefficients and variable selection when both the response and covariates are It\^o semimartingales with jumps. The coefficient paths are…

We study the properties of an approximation of the Laplace operator with Neumann boundary conditions using volume penalization. For the one-dimensional Poisson equation we compute explicitly the exact solution of the penalized equation and…

In this paper we study regularity estimates for the solution to an obstacle problem arising in stochastic impulse control theory. We prove using elementary methods the known sharp $C_{loc}^{1,1}$ estimate for the solution. The new proof is…

In this article we consider the problem of finding the visibility set from a given point when the obstacles are represented as the level set of a given function. Although the visibility set can be computed efficiently by ray tracing, there…

We analyze the limit behavior as $s\to 1^-$ of the solution to the fractional Poisson equation $(-\Delta)^s u_s=f_s$, $x\in\Omega$ with homogeneous Dirichlet boundary conditions $u_s\equiv 0$, $x\in\Omega^c$. We show that $\lim_{s\to 1^-}…

This paper studies sparse linear regression analysis with outliers in the responses. A parameter vector for modeling outliers is added to the standard linear regression model and then the sparse estimation problem for both coefficients and…

In this paper, motivated by a problem in stochastic impulse control theory, we aim to study solutions to a free boundary problem of obstacle-type. We obtain sharp estimates for the solution using nonlinear tools which are independent of the…

This work proposes new estimators for discrete optimal transport plans that enjoy Gaussian limits centered at the true solution. This behavior stands in stark contrast with the performance of existing estimators, including those based on…

We study the obstacle problem for the fractional Laplacian with drift, $\min\left\{(-\Delta)^s u + b \cdot \nabla u,\,u -\varphi\right\} = 0$ in $\mathbb{R}^n$, in the critical regime $s = \frac{1}{2}$. Our main result establishes the…

The solution to the initial and Dirichlet boundary value problem for a semilinear, one dimensional heat equation is approximated by a numerical method that combines the Besse relaxation scheme in time (C. R. Acad. Sci. Paris S{\'e}r. I,…

We analyse the obstacle problem for the nonlocal parabolic operator \[\partial_t u + (-\Delta)^{s} u - b \cdot \nabla u - \mathcal{I}u - ru,\] where $b\in\mathbb{R}^n$, $r\in\mathbb{R}$, and $\mathcal{I}$ is a nonlocal lower order diffusion…

This paper gives a comprehensive treatment of the convergence rates of penalized spline estimators for simultaneously estimating several leading principal component functions, when the functional data is sparsely observed. The penalized…

This paper focuses on the problem of the estimation of the cumulative hazard function of a distribution on a general complete separable metric space when the data points are subject to censoring by an arbitrary adapted random set. A problem…

Despite significant recent advances in the regularity theory for obstacle problems with integro-differential operators, some fundamental questions remained open. On the one hand, there was a lack of understanding of parabolic problems with…

We obtain sharp convergence rates, using Dirichlet correctors, for solutions of wave equations in a bounded domain with rapidly oscillating periodic coefficients. The results are used to prove the exact boundary controllability that is…

We develop a uniform inference theory for high-dimensional slope parameters in threshold regression models, allowing for either cross-sectional or time series data. We first establish oracle inequalities for prediction errors, and L1…

We discretize the Lagrange multiplier formulation of the obstacle problem by mixed and stabilized finite element methods. A priori and a posteriori error estimates are derived and numerically verified.

Many problems in classification involve huge numbers of irrelevant features. Model selection reveals the crucial features, reduces the dimensionality of feature space, and improves model interpretation. In the support vector machine…

We consider a non-homogeneous generalised Burgers equation: $$ \frac{\partial u}{\partial t} + f'(u)\frac{\partial u}{\partial x} - \nu \frac{\partial^2 u}{\partial x^2} = \eta^{\omega},\quad t \in \R,\ x \in S^1. $$ Here, \nu is small and…

In this paper we treat the numerical approximation of the two-phase parabolic obstacle-like problem: \[\Delta u -u_t=\lambda^+\cdot\chi_{\{u>0\}}-\lambda^-\cdot\chi_{\{u<0\}},\quad (t,x)\in (0,T)\times\Omega,\] where $T < \infty, \lambda^+…