Related papers: On boundary detection
Distance correlation is a measure of dependence between two paired random vectors or matrices of arbitrary, not necessarily equal, dimensions. Unlike Pearson correlation, the population distance correlation coefficient is zero if and only…
Let $X_1,X_2, \ldots $ be independent random uniform points in a bounded domain $A \subset \mathbb{R}^d$ with smooth boundary. Define the coverage threshold $R_n$ to be the smallest $r$ such that $A$ is covered by the balls of radius $r$…
We address the problem of learning an unknown smooth function and its derivatives from noisy pointwise evaluations under the supremum norm. While classical nonparametric regression provides a strong theoretical foundation, traditional…
We formulate nonparametric and semiparametric hypothesis testing of multivariate stationary linear time series in a unified fashion and propose new test statistics based on estimators of the spectral density matrix. The limiting…
For many causal effect parameters of interest, doubly robust machine learning (DRML) estimators $\hat{\psi}_{1}$ are the state-of-the-art, incorporating the good prediction performance of machine learning; the decreased bias of doubly…
A variety of statistics based on sample spacings has been studied in the literature for testing goodness-of-fit to parametric distributions. To test the goodness-of-fit to a nonparametric class of univariate shape-constrained densities,…
Motivated by a wide variety of applications, ranging from stochastic optimization to dimension reduction through variable selection, the problem of estimating gradients accurately is of crucial importance in statistics and learning theory.…
We study the problem of estimating, in the sense of optimal transport metrics, a measure which is assumed supported on a manifold embedded in a Hilbert space. By establishing a precise connection between optimal transport metrics, optimal…
We study obstacle problems governed by two distinct types of diffusion operators involving interacting free boundaries. We obtain a somewhat surprising coupling property, leading to a comprehensive analysis of the free boundary. More…
We start the investigation of free boundary variational models featuring varying singularities. The theory depends strongly on the nature of the singular power $\gamma(x)$ and how it changes. Under a mild continuity assumption on…
Consider a graph with a set of vertices and oriented edges connecting pairs of vertices. Each vertex is associated with a random variable and these are assumed to be independent. In this setting, suppose we wish to solve the following…
This paper introduces an innovative method for conducting conditional independence testing in high-dimensional data, facilitating the automated discovery of significant associations within distinct subgroups of a population, all while…
In this paper we investigate the problem of testing the assumption of stationarity in locally stationary processes. The test is based on an estimate of a Kolmogorov-Smirnov type distance between the true time varying spectral density and…
This paper introduces the \textit{weighted partial copula} function for testing conditional independence. The proposed test procedure results from these two ingredients: (i) the test statistic is an explicit Cramer-von Mises transformation…
In model-based testing (MBT) we may have to deal with a non-deterministic model, e.g. because abstraction was applied, or because the software under test itself is non-deterministic. The same test case may then trigger multiple possible…
With the aid of the concept of stable independence we can construct, in an efficient way, a compact representation of a semi-graphoid independence relation. We show that this representation provides a new necessary condition for the…
We consider the problem of bounding away from 0 the minimum value m taken by a polynomial P of Z[X_1,...,X_k] over the standard simplex, assuming that m>0. Recent algorithmic developments in real algebraic geometry enable us to obtain a…
In hypothesis testing problems the property of strict unbiasedness describes whether a test is able to discriminate, in the sense of a difference in power, between any distribution in the null hypothesis space and any distribution in the…
The simple and partial Mantel tests are routinely used in many areas of evolutionary biology to assess the significance of the association between two or more matrices of distances relative to the same pairs of individuals or demes. Partial…
A statistical test based on the geometric mean is proposed to determine if a predictive model should be rejected or not, when the quantity of interest is a strictly positive continuous random variable. A simulation study is performed to…