Related papers: Block Sampling under Strong Dependence
In this note we consider sampling from (non-homogeneous) strongly Rayleigh probability measures. As an important corollary, we obtain a fast mixing Markov Chain sampler for Determinantal Point Processes.
A variety of methods have been proposed for inference about extreme dependence for multivariate or spatially-indexed stochastic processes and time series. Most of these proceed by first transforming data to some specific extreme value…
Limit theorems for non-additive probabilities or non-linear expectations are challenging issues which have raised progressive interest recently. The purpose of this paper is to study the strong law of large numbers and the law of the…
Long-range dependence and non-Gaussianity are ubiquitous in many natural systems like ecosystems, biological systems and climate. However, it is not always appreciated that both phenomena may occur together in natural systems and that…
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…
A determinantal point process is a stochastic point process that is commonly used to capture negative correlations. It has become increasingly popular in machine learning in recent years. Sampling a determinantal point process however…
We have developed a linearization method to investigate the subthreshold oscillatory behaviors in nonlinear autonomous systems. By considering firstly the neuronal system as an example, we show that this theoretical approach can predict…
One reason why standard formulations of the central limit theorems are not applicable in high-dimensional and non-stationary regimes is the lack of a suitable limit object. Instead, suitable distributional approximations can be used, where…
For temporal regularly spaced datasets, a lot of methods are available and the properties of these methods are extensively investigated. Less research has been performed on irregular temporal datasets subject to measurement error with…
In this paper, we focus on the problem of statistical dependence estimation using characteristic functions. We propose a statistical dependence measure, based on the maximum-norm of the difference between joint and product-marginal…
We present a tractable non-independent increment process which provides a high modeling flexibility. The process lies on an extension of the so-called Harris chains to continuous time being stationary and Feller. We exhibit constructions,…
We describe an algorithm to quantify dependence in a multivariate data set. The algorithm is able to identify any linear and non-linear dependence in the data set by performing a hypothesis test for two variables being independent. As a…
Cluster indices describe extremal behaviour of stationary time series. We consider their sliding blocks estimators. Using a modern theory of multivariate, regularly varying time series, we obtain central limit theorems under conditions that…
In this paper, an estimator of $m$ instants ($m$ is known) of abrupt changes of the parameter of long-range dependence or self-similarity is proved to satisfy a limit theorem with an explicit convergence rate for a sample of a Gaussian…
Under a complex technical condition, similar to such used in extreme value theory, we find the rate q(\epsilon)^{-1} at which a stochastic process with stationary increments \xi should be sampled, for the sampled process \xi(\lfloor\cdot…
The use of random sampling in decision-making and control has become popular with the ease of access to graphic processing units that can generate and calculate multiple random trajectories for real-time robotic applications. In contrast to…
A family of self-similar and translation-invariant random sup-measures with long-range dependence are investigated. They are shown to arise as the limit of the empirical random sup-measure of a stationary heavy-tailed process, inspired by…
Drawing a sample from a discrete distribution is one of the building components for Monte Carlo methods. Like other sampling algorithms, discrete sampling suffers from the high computational burden in large-scale inference problems. We…
We study a special case of the problem of statistical learning without the i.i.d. assumption. Specifically, we suppose a learning method is presented with a sequence of data points, and required to make a prediction (e.g., a classification)…
The paper presents a systematic theory for asymptotic inference of autocovariances of stationary processes. We consider nonparametric tests for serial correlations based on the maximum (or ${\cal L}^\infty$) and the quadratic (or ${\cal…