Related papers: Uniform Convergence Rate of the Nonparametric Esti…
Subordinate diffusions are constructed by time changing diffusion processes with an independent L\'{e}vy subordinator. This is a rich family of Markovian jump processes which exhibit a variety of jump behavior and have found many…
We propose a method for approximating the large deviation rate function of time-integrated observables of diffusion processes, used in statistical physics to characterize the fluctuations of nonequilibrium systems. The method is based on…
This paper considers the practically important case of nonparametrically estimating heterogeneous average treatment effects that vary with a limited number of discrete and continuous covariates in a selection-on-observables framework where…
Deep nonparametric regression, characterized by the utilization of deep neural networks to learn target functions, has emerged as a focus of research attention in recent years. Despite considerable progress in understanding convergence…
Weighting methods are essential tools for estimating causal effects in observational studies, with the goal of balancing pre-treatment covariates across treatment groups. Traditional approaches pursue this objective indirectly, for example,…
We provide a general method to analyze the asymptotic properties of a variety of estimators of continuous time diffusion processes when the data are not only discretely sampled in time but the time separating successive observations may…
We introduce verifiable criteria for weak posterior consistency of identifiable Bayesian nonparametric inference for jump diffusions with unit diffusion coefficient and uniformly Lipschitz drift and jump coefficients in arbitrary dimension.…
The statistical analysis of covariance matrices occurs in many important applications, e.g. in diffusion tensor imaging and longitudinal data analysis. We consider the situation where it is of interest to estimate an average covariance…
Inferring models, predicting the future, and estimating the entropy rate of discrete-time, discrete-event processes is well-worn ground. However, a much broader class of discrete-event processes operates in continuous-time. Here, we provide…
This paper is devoted to the estimators of the mean that provide strong non-asymptotic guarantees under minimal assumptions on the underlying distribution. The main ideas behind proposed techniques are based on bridging the notions of…
Part I of this work [2] developed the exact diffusion algorithm to remove the bias that is characteristic of distributed solutions for deterministic optimization problems. The algorithm was shown to be applicable to a larger set of…
We propose two classes of nonparametric point estimators of $\theta=P(X<Y)$ in the case where $(X,Y)$ are paired, possibly dependent, absolutely continuous random variables. The proposed estimators are based on nonparametric estimators of…
This paper is the second part of the study. In Part~I, self-similar solutions of a weighted fast diffusion equation (WFD) were related to optimal functions in a family of subcritical Caffarelli-Kohn-Nirenberg inequalities (CKN) applied to…
This study introduces a debiasing method for regression estimators, including high-dimensional and nonparametric regression estimators. For example, nonparametric regression methods allow for the estimation of regression functions in a…
We consider nonparametric invariant density and drift estimation for a class of multidimensional degenerate resp. hypoelliptic diffusion processes, so-called stochastic damping Hamiltonian systems or kinetic diffusions, under anisotropic…
We present new gradient estimates and Harnack inequalities for positive solutions to nonlinear slow diffusion equations. The framework is that of a smooth metric measure space $(\mathscr M,g,d\mu)$ with invariant weighted measure…
In this article we consider the development of unbiased estimators of the Hessian, of the log-likelihood function with respect to parameters, for partially observed diffusion processes. These processes arise in numerous applications, where…
We consider a collection of fully coupled weakly interacting diffusion processes moving in a two-scale environment. We study the moderate deviations principle of the empirical distribution of the particles' positions in the combined limit…
Diffusion models, which convert noise into new data instances by learning to reverse a Markov diffusion process, have become a cornerstone in contemporary generative modeling. While their practical power has now been widely recognized, the…
In this paper, we study the diffusion approximation for singularly perturbed stochastic reaction-diffusion equation with a fast oscillating term. The asymptotic limit for the original system is obtained, where an extra Gaussian term…