Related papers: Concentration inequalities for the sample correlat…
We place ourselves in the setting of high-dimensional statistical inference, where the number of variables $p$ in a data set of interest is of the same order of magnitude as the number of observations $n$. More formally, we study the…
We prove a new and general concentration inequality for the excess risk in least-squares regression with random design and heteroscedastic noise. No specific structure is required on the model, except the existence of a suitable function…
Simulating sample correlation matrices is important in many areas of statistics. Approaches such as generating Gaussian data and finding their sample correlation matrix or generating random uniform $[-1,1]$ deviates as pairwise correlations…
We investigate the properties of a sequential Monte Carlo method where the particle weight that appears in the algorithm is estimated by a positive, unbiased estimator. We present broadly-applicable convergence results, including a central…
In the statistical inference for long range dependent time series the shape of the limit distribution typically depends on unknown parameters. Therefore, we propose to use subsampling. We show the validity of subsampling for general…
We consider the semi-parametric estimation of a scale parameter of a one-dimensional Gaussian process with known smoothness. We suggest an estimator based on quadratic variations and on the moment method. We provide asymptotic…
Probability density estimation is a core problem of statistics and signal processing. Moment methods are an important means of density estimation, but they are generally strongly dependent on the choice of feasible functions, which severely…
In this paper we first provide a method to compute confidence intervals for the center of a piecewise normal distribution given a sample from this distribution, under certain assumptions. We then extend this method to an asymptotic setting,…
Consider two random variables contaminated by two unknown transformations. The aim of this paper is to test the equality of those transformations. Two cases are distinguished: first, the two random variables have known distributions.…
Estimating the unknown density from which a given independent sample originates is more difficult than estimating the mean, in the sense that for the best popular non-parametric density estimators, the mean integrated square error converges…
This paper considers inference for conditional moment inequality models using a multiscale statistic. We derive the asymptotic distribution of this test statistic and use the result to propose feasible critical values that have a simple…
We provide finite-sample distribution approximations, that are uniform in the parameter, for inference in linear mixed models. Focus is on variances and covariances of random effects in cases where existing theory fails because their…
We investigate the asymptotic properties of Bayesian bivariate causal discovery for Gaussian Linear Structural Equation Models (SEMs) with heteroscedastic noise. We demonstrate that with purely observational data, the posterior distribution…
Chatterjee's correlation coefficient has recently been proposed as a new association measure for bivariate random vectors that satisfies a number of desirable properties. Among these properties is the feature that the coefficient equals one…
We consider the Dirac equation in $\R^3$ with constant coefficients and study the distribution $\mu_t$ of the random solution at time $t\in\R$. It is assumed that the initial measure $\mu_0$ has zero mean, a translation-invariant…
There has been much interest in the nonparametric testing of conditional independence in the econometric and statistical literature, but the simplest and potentially most useful method, based on the sample partial correlation, seems to have…
Context. Whenever correlation functions are used for inference about cosmological parameters in the context of a Bayesian analysis, the likelihood function of correlation functions needs to be known. Usually, it is approximated as a…
In this paper, we revisit the notion of partial copula, originally introduced to test conditional independence, highlighting its capability to represent the dependence between two random variables after removing their dependence with a…
In this paper we explore partial coherence as a tool for evaluating causal influence of one signal sequence on another. In some cases the signal sequence is sampled from a time- or space-series. The key idea is to establish a connection…
We derive novel anti-concentration bounds for the difference between the maximal values of two Gaussian random vectors across various settings. Our bounds are dimension-free, scaling with the dimension of the Gaussian vectors only through…