Related papers: A varifold-type estimation for data sampled on a r…

In increasingly many settings, data sets consist of multiple samples from a population of networks, with vertices aligned across these networks. For example, brain connectivity networks in neuroscience consist of measures of interaction…

We estimate from below the expected Betti numbers of real hypersurfaces taken at random in a smooth real projective n-dimensional manifold. These random hypersurfaces are chosen in the linear system of a large d-th power of a real ample…

In the framework of shape constrained estimation, we review methods and works done in convex set estimation. These methods mostly build on stochastic and convex geometry, empirical process theory, functional analysis, linear programming,…

In statistical dimensionality reduction, it is common to rely on the assumption that high dimensional data tend to concentrate near a lower dimensional manifold. There is a rich literature on approximating the unknown manifold, and on…

We introduce a new variational estimator for the intensity function of an inhomogeneous spatial point process with points in the $d$-dimensional Euclidean space and observed within a bounded region. The variational estimator applies in a…

Consider the random matrix $\Sigma = D^{1/2} X \widetilde D^{1/2}$ where $D$ and $\widetilde D$ are deterministic Hermitian nonnegative matrices with respective dimensions $N \times N$ and $n \times n$, and where $X$ is a random matrix with…

If one considers an integral varifold $I^m\subseteq M$ with bounded mean curvature, and if $S^k(I)\equiv\{x\in M: \text{ no tangent cone at $x$ is }k+1\text{-symmetric}\}$ is the standard stratification of the singular set, then it is well…

We introduce Riemannian-like structures associated with strong local Dirichlet forms on general state spaces. Such structures justify the principle that the pointwise index of the Dirichlet form represents the effective dimension of the…

We present a local density estimator based on first order statistics. To estimate the density at a point, $x$, the original sample is divided into subsets and the average minimum sample distance to $x$ over all such subsets is used to…

We consider the deconvolution problem for densities supported on a $(d-1)$-dimensional sphere with unknown center and unknown radius, in the situation where the distribution of the noise is unknown and without any other observations. We…

Kernel density estimators with circular data have been studied extensively for decades, as they allow flexible estimations even when the shape of the underlying density is complex. Many recent studies have examined bias correction methods;…

We introduce a construction of multiscale tight frames on general domains. The frame elements are obtained by spectral filtering of the integral operator associated with a reproducing kernel. Our construction extends classical wavelets as…

We consider the problem of recovering a $d-$dimensional manifold $\mathcal{M} \subset \mathbb{R}^n$ when provided with noiseless samples from $\mathcal{M}$. There are many algorithms (e.g., Isomap) that are used in practice to fit manifolds…

Convergence rates of kernel density estimators for stationary time series are well studied. For invertible linear processes, we construct a new density estimator that converges, in the supremum norm, at the better, parametric, rate…

When observations are truncated, we are limited to an incomplete picture of our dataset. Recent methods propose to use score matching for truncated density estimation, where the access to the intractable normalising constant is not…

Let $K$ be a convex body in $\R^d$, let $j\in\{1, ..., d-1\}$, and let $\varrho$ be a positive and continuous probability density function with respect to the $(d-1)$-dimensional Hausdorff measure on the boundary $\partial K$ of $K$. Denote…

We consider the problem of reconstructing the intrinsic geometry of a manifold from noisy pairwise distance observations. Specifically, let $M$ denote a diameter 1 d-dimensional manifold and $\mu$ a probability measure on $M$ that is…

For any $Q\in\{\frac{3}{2},2,\frac{5}{2},3,\dotsc\}$, we establish a structure theory for the class $\mathcal{S}_Q$ of stable codimension 1 stationary integral varifolds admitting no classical singularities of density $<Q$. This theory…

In this paper, we study a smoothness regularization method for a varying coefficient model based on sparse and irregularly sampled functional data which is contaminated with some measurement errors. We estimate the one-dimensional…

This paper develops a variance estimation framework for matching estimators that enables valid population inference for treatment effects. We provide theoretical analysis of a variance estimator that addresses key limitations in the…