Related papers: A note on the empirical process of strongly depend…
Strong invariance principles describe the error term of a Brownian approximation of the partial sums of a stochastic process. While these strong approximation results have many applications, the results for continuous-time settings have…
In this paper we investigate the parametric inference for the linear fractional stable motion in high and low frequency setting. The symmetric linear fractional stable motion is a three-parameter family, which constitutes a natural…
Recently there has been an increasing interest in methods that deal with multiple outputs. This has been motivated partly by frameworks like multitask learning, multisensor networks or structured output data. From a Gaussian processes…
The declining response rates in probability surveys along with the widespread availability of unstructured data has led to growing research into non-probability samples. Existing robust approaches are not well-developed for non-Gaussian…
Max-stable processes have proved to be useful for the statistical modelling of spatial extremes. Several representations of max-stable random fields have been proposed in the literature. For statistical inference it is often assumed that…
We investigate the frequentist guarantees of the variational sparse Gaussian process regression model. In the theoretical analysis, we focus on the variational approach with spectral features as inducing variables. We derive guarantees and…
Probabilistic regression models typically use the Maximum Likelihood Estimation or Cross-Validation to fit parameters. These methods can give an advantage to the solutions that fit observations on average, but they do not pay attention to…
We study statistical inference for small-noise-perturbed multiscale dynamical systems. We prove consistency, asymptotic normality, and convergence of all scaled moments of an appropriately-constructed maximum likelihood estimator (MLE) for…
In the regression framework, the empirical measure based on the responses resulting from the nearest neighbors, among the covariates, to a given point $x$ is introduced and studied as a central statistical quantity. First, the associated…
We define generalized innovations associated with generalized error models having arbitrary distributions, that is, distributions that can be mixtures of continuous and discrete distributions. These models include stochastic volatility…
Generalized linear statistics are an unifying class that contains U-statistics, U-quantiles, L-statistics as well as trimmed and winsorized U-statistics. For example, many commonly used estimators of scale fall into this class.…
We address the issue of semiparametric efficiency in the bivariate regression problem with a highly persistent predictor, where the joint distribution of the innovations is regarded an infinite-dimensional nuisance parameter. Using a…
Motivated by some common-change point tests, we investigate the asymptotic distribution of the U-statistic process $U_n(t)=\sum_{i=1}^{[nt]}\sum_{j=[nt]+1}^n h(X_i,X_j)$, $0\leq t\leq 1$, when the underlying data are long-range dependent.…
In this paper we propose and study a general class of Gaussian Semiparametric Estimators (GSE) of the fractional differencing parameter in the context of long-range dependent multivariate time series. We establish large sample properties of…
We revisit the Kolmogorov-Smirnov and Cram\'er-von Mises goodness-of-fit (GoF) tests and propose a generalisation to identically distributed, but dependent univariate random variables. We show that the dependence leads to a reduction of the…
We investigate the hyperuniformity of marked Gibbs point processes with weak dependencies among distant points whilst the interactions of close points are kept arbitrary. Some variants of stability and range assumptions are posed on the…
We consider maximum likelihood estimation with data from a bivariate Gaussian process with a separable exponential covariance model under fixed domain asymptotic. We first characterize the equivalence of Gaussian measures under this model.…
For time series with high temporal correlation, the empirical process converges rather slowly to its limiting distribution. Many statistics in change-point analysis, goodness-of-fit testing and uncertainty quantification admit a…
We study the empirical measure associated to a sample of size $n$ and modified by $N$ iterations of the raking-ratio method. This empirical measure is adjusted to match the true probability of sets in a finite partition which changes each…
Several important families of computational and statistical results in machine learning and randomized algorithms rely on uniform bounds on quadratic forms of random vectors or matrices. Such results include the Johnson-Lindenstrauss (J-L)…