相关论文: Identification d'un processus autor\'{e}gressif ga…

In this note, we give a short information-theoretic proof of the consistency of the Gaussian maximum likelihood estimator in linear auto-regressive models. Our proof yields nearly optimal non-asymptotic rates for parameter recovery and…

From a wavelet analysis, one derives a nonparametrical estimator for the spectral density of a Gaussian process with stationary increments. First, the idealistic case of a continuous time path of the process is considered. A punctual…

This paper introduces a new kind of seasonal fractional autoregressive process (SFAR) driven by fractional Gaussian noise (fGn). The new model includes a standard seasonal AR model and fGn. {The estimation of the parameters of this new…

We present a novel extension of multi-output Gaussian processes for handling heterogeneous outputs. We assume that each output has its own likelihood function and use a vector-valued Gaussian process prior to jointly model the parameters in…

In this article, normal inverse Gaussian (NIG) autoregressive model is introduced. The parameters of the model are estimated using Expectation Maximization (EM) algorithm. The efficacy of the EM algorithm is shown using simulated and real…

The paper considers the problem to estimate non-causal graphical models whose edges encode smoothing relations among the variables. We propose a new covariance extension problem and show that the solution minimizing the transportation…

Discretization of continuous stochastic processes is needed to numerically simulate them or to infer models from experimental time series. However, depending on the nature of the process, the same discretization scheme, if not accurate…

In this paper we study the spatial averages of the solution of a one-dimensional stochastic wave equation driven by a Gaussian multiplicative noise, which is white in time and has a homogeneous spatial covariance described by the Riesz…

Stochastic processes are a flexible and widely used family of models for statistical modeling. While stochastic processes offer attractive properties such as inclusion of uncertainty properties, their inference is typically intractable,…

Various approaches to stochastic processes exist, noting that key properties such as measurability and continuity are not trivially satisfied. We introduce a new theory for Gaussian processes using improper linear functionals. Using a…

Bayesian approach to inverse problems is studied in the case where the forward map is a linear hypoelliptic pseudodifferential operator and measurement error is additive white Gaussian noise. The measurement model for an unknown Gaussian…

Accurately estimating the statistical properties of noise is important in data analysis for space-based gravitational wave detectors. Noise in different time-delay interferometry channels correlates with each other. Many studies often…

An extension and generalization of a recently presented approach for the analysis of Langevin-type stochastic processes in the presence of strong measurement noise is presented. For a stochastic process in N dimensions which is superimposed…

We propose a generalized debiased Lasso estimator based on a stability principle. When a single column of the design matrix is perturbed, the estimator admits a simple update formula that can be computed from the original solution. Under…

A popular class of problem in statistics deals with estimating the support of a density from $n$ observations drawn at random from a $d$-dimensional distribution. The one-dimensional case reduces to estimating the end points of a univariate…

In magnetoencephalography (MEG) the conventional approach to source reconstruction is to solve the underdetermined inverse problem independently over time and space. Here we present how the conventional approach can be extended by…

Stochastic averaging problems with Gaussian forcing have been studied thoroughly for many years, but far less attention has been paid to problems where the stochastic forcing has infinite variance, such as an {\alpha}-stable noise forcing.…

Geographical and Temporal Weighted Regression (GTWR) model is an important local technique for exploring spatial heterogeneity in data relationships, as well as temporal dependence due to its high fitting capacity when it comes to real…

A continuous approximation framework for non-linear stochastic as well as deterministic discrete maps is developed. For the stochastic map with uncorelated Gaussian noise, by successively applying the It\^o lemma, we obtain a Langevin type…

We focus on estimating the integrated covariance of log-price processes in the presence of market microstructure noise. We construct an efficient unbiased estimator for the quadratic covariation of two It\^{o} processes in the case where…