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Discrete time trawl processes constitute a large class of time series parameterized by a trawl sequence (a j) j$\in$N and defined though a sequence of independent and identically distributed (i.i.d.) copies of a continuous time process…

Statistics Theory · Mathematics 2020-01-09 Paul Doukhan , François Roueff , Joseph Rynkiewicz

The problem of finding the expected value of a statistic of a locally stable point process in a bounded region is addressed. We propose an adaptive importance sampling for solving the problem. In our proposal, we restrict the importance…

Machine Learning · Statistics 2025-03-04 Hee-Geon Kang , Sunggon Kim

We develop a theory of optimal transport for stationary random measures with a focus on stationary point processes and construct a family of distances on the set of stationary random measures. These induce a natural notion of interpolation…

Probability · Mathematics 2024-02-02 Matthias Erbar , Martin Huesmann , Jonas Jalowy , Bastian Müller

Time series classification is crucial for numerous scientific and engineering applications. In this article, we present a numerically efficient, practically competitive, and theoretically rigorous classification method for distinguishing…

Methodology · Statistics 2025-07-11 Chen Qian , Xiucai Ding , Lexin Li

We consider a measurable stationary Gaussian stochastic process. A criterion for testing hypotheses about the covariance function of such a process using estimates for its norm in the space $L_p(\mathbb {T}),\,p\geq1$, is constructed.

Probability · Mathematics 2015-03-19 Yuriy Kozachenko , Viktor Troshki

The periodogram is a widely used tool to analyze second order stationary time series. An attractive feature of the periodogram is that the expectation of the periodogram is approximately equal to the underlying spectral density of the time…

Statistics Theory · Mathematics 2020-11-03 Sourav Das , Suhasini Subba Rao , Junho Yang

In the matter of selection of sample time points for the estimation of the power spectral density of a continuous time stationary stochastic process, irregular sampling schemes such as Poisson sampling are often preferred over regular…

Statistics Theory · Mathematics 2010-07-19 Radhendushka Srivastava , Debasis Sengupta

In this paper, we study the problem of adaptive estimation of the spectral density of a stationary Gaussian process. For this purpose, we consider a wavelet-based method which combines the ideas of wavelet approximation and estimation by…

Statistics Theory · Mathematics 2011-06-07 Jérémie Bigot , Rolando Biscay Lirio , Jean-Michel Loubes , Lilian Muniz Alvarez

Some convergence results on the kernel density estimator are proven for a class of linear processes with cyclical effects. In particular we extend the results of Ho and Hsing (1996a) and Mielniczuk (1997) to the stationary processes for…

Statistics Theory · Mathematics 2011-04-18 Mohamedou Ould Haye , Anne Philippe

We propose a data-driven method to learn the time-dependent probability density of a multivariate stochastic process from sample paths, assuming that the initial probability density is known and can be evaluated. Our method uses a novel…

Machine Learning · Statistics 2025-06-19 Agnimitra Dasgupta , Javier Murgoitio-Esandi , Ali Fardisi , Assad A Oberai

Existing frequency domain methods for bootstrapping time series have a limited range. Consider for instance the class of spectral mean statistics (also called integrated periodograms) which includes many important statistics in time series…

Methodology · Statistics 2018-06-19 Marco Meyer , Efstathios Paparoditis , Jens-Peter Kreiss

The distance covariance of two random vectors is a measure of their dependence. The empirical distance covariance and correlation can be used as statistical tools for testing whether two random vectors are independent. We propose an analogs…

Statistics Theory · Mathematics 2017-03-31 Muneya Matsui , Thomas Mikosch , Gennady Samorodnitsky

A new bivariate partial sum process for locally stationary time series is introduced and its weak convergence to a Brownian sheet is established. This construction enables the development of a novel self-normalized CUSUM test statistic for…

Statistics Theory · Mathematics 2026-04-15 Florian Heinrichs

We present an efficient and validated method for approximating the stationary measures of random dynamical systems with smooth additive noise. The approach leverages the strong regularizing properties of the associated transfer operator…

Dynamical Systems · Mathematics 2026-02-24 Stefano Galatolo , Charles Lopez Vereau , Luigi Marangio , Isaia Nisoli

Numerical approximation of the long time behavior of a stochastic differential equation (SDE) is considered. Error estimates for time-averaging estimators are obtained and then used to show that the stationary behavior of the numerical…

Probability · Mathematics 2013-11-26 Jonathan C. Mattingly , Andrew M. Stuart , M. V. Tretyakov

The analysis of continuously spatially varying processes usually considers two sources of variation, namely, the large-scale variation collected by the trend of the process, and the small-scale variation. Parametric trend models on latitude…

We introduce an index based on information theory to quantify the stationarity of a stochastic process.The index compares on the one hand the information contained in the increment at the time scale $\tau$ of the process at time $t$ with,…

Data Analysis, Statistics and Probability · Physics 2021-12-02 Carlos Granero-Belinchon , Stéphane G. Roux , Nicolas B. Garnier

In this paper, we focus on activating only a few sensors, among many available, to estimate the state of a stochastic process of interest. This problem is important in applications such as target tracking and simultaneous localization and…

Systems and Control · Computer Science 2016-09-28 Vasileios Tzoumas , Nikolay A. Atanasov , Ali Jadbabaie , George J. Pappas

Distance metric learning is a successful way to enhance the performance of the nearest neighbor classifier. In most cases, however, the distribution of data does not obey a regular form and may change in different parts of the feature…

Computer Vision and Pattern Recognition · Computer Science 2018-03-19 Hossein Rajabzadeh , Mansoor Zolghadri Jahromi , Mohammad Sadegh Zare , Mostafa Fakhrahmad

We propose an algorithm to estimate the common density $s$ of a stationary process $X_1,...,X_n$. We suppose that the process is either $\beta$ or $\tau$-mixing. We provide a model selection procedure based on a generalization of Mallows'…

Statistics Theory · Mathematics 2009-09-08 Matthieu Lerasle