Related papers: Nadaraya-Watson Type Estimator of the Transition D…
We introduce a new approach for estimating the invariant density of a multidimensional diffusion when dealing with high-frequency observations blurred by independent noises. We consider the intermediate regime, where observations occur at…
In this paper we prove large deviations principles for the Nadaraya-Watson estimator of the regression of a real-valued variable with a functional covariate. Under suitable conditions, we show pointwise and uniform large deviations theorems…
In this paper we propose a variable bandwidth kernel regression estimator for $i.i.d.$ observations in $\mathbb{R}^2$ to improve the classical Nadaraya-Watson estimator. The bias is improved to the order of $O(h_n^4)$ under the condition…
We study a discrete denoising diffusion framework that integrates a sample-efficient estimator of single-site conditionals with round-robin noising and denoising dynamics for generative modeling over discrete state spaces. Rather than…
We adapt and extend Yosida's parametrix method, originally introduced for the construction of the fundamental solution to a parabolic operator on a Riemannian manifold, to derive Varadhan-type asymptotic estimates for the transition density…
This paper addresses the nonparametric estimation of the drift function over a compact domain for a time-homogeneous diffusion process, based on high-frequency discrete observations from $N$ independent trajectories. We propose a neural…
We propose a test for model specification of a parametric diffusion process based on a kernel estimation of the transitional density of the process. The empirical likelihood is used to formulate a statistic, for each kernel smoothing…
This paper obtains asymptotic results for parametric inference using prediction-based estimating functions when the data are high frequency observations of a diffusion process with an infinite time horizon. Specifically, the data are…
This paper presents new results on the Edgeworth expansion for high frequency functionals of continuous diffusion processes. We derive asymptotic expansions for weighted functionals of the Brownian motion and apply them to provide the…
We consider statistical inference for parameters defined by general estimating equations under the covariate shift transfer learning. Different from the commonly used density ratio weighting approach, we undertake a set of formulations to…
We investigate the moment estimation for an ergodic diffusion process with unknown trend coefficient. We consider nonparametric and parametric estimation. In each case, we present a lower bound for the risk and then construct an…
This paper considers the problem of adaptive estimation of a non-homogeneous intensity function from the observation of n independent Poisson processes having a common intensity that is randomly shifted for each observed trajectory. We show…
Inferring a diffusion equation from discretely-observed measurements is a statistical challenge of significant importance in a variety of fields, from single-molecule tracking in biophysical systems to modeling financial instruments.…
We study nonparametric estimation of the diffusion coefficient from discrete data, when the observations are blurred by additional noise. Such issues have been developed over the last 10 years in several application fields and in particular…
The paper deals with the statistical analysis of several data sets associated with shape invariant models with different translation, height and scaling parameters. We propose to estimate these parameters together with the common shape…
This work presents a non-parametric estimator for the cumulative distribution function (CDF) of the job-size distribution for a queue with compound Poisson input. The workload process is observed according to an independent Poisson sampling…
Functional time series (FTS) extend traditional methodologies to accommodate data observed as functions/curves. A significant challenge in FTS consists of accurately capturing the time-dependence structure, especially with the presence of…
This paper proposes a widely applicable method of approximate maximum-likelihood estimation for multivariate diffusion process from discretely sampled data. A closed-form asymptotic expansion for transition density is proposed and…
Biophysical modelling of the diffusion MRI signal provides estimates of specific microstructural tissue properties. Although nonlinear optimization such as non-linear least squares (NLLS) is the most widespread method for model estimation,…
In this paper we propose a convolution estimator for estimating the density of a response variable that employs an underlying multiple regression framework to enhance the accuracy of density estimates through the incorporation of auxiliary…