Related papers: Nonparametric Density Estimation under Distributio…

In this article, we consider a jump diffusion process (X_t)observed at discrete times t=0,Delta,...,nDelta. The sampling interval Delta tends to 0 and nDelta tends to infinity. We assume that (X_t) is ergodic, strictly stationary and…

We study the estimation of time-homogeneous drift functions in multivariate stochastic differential equations with known diffusion coefficient, from multiple trajectories observed at high frequency over a fixed time horizon. We formulate…

This work addresses various open questions in the theory of active learning for nonparametric classification. Our contributions are both statistical and algorithmic: -We establish new minimax-rates for active learning under common…

While many real-world data streams imply that they change frequently in a nonstationary way, most of deep learning methods optimize neural networks on training data, and this leads to severe performance degradation when dataset shift…

We consider a nonparametric goodness of fit test problem for the drift coefficient of one-dimensional small diffusions. Our test is based on discrete observation of the processes, and the diffusion coefficient is a nuisance function which…

In the context of nonparametric regression, we study conditions under which the consistency (and rates of convergence) of estimators built from discretely sampled curves can be derived from the consistency of estimators based on the…

We study the maximum likehood estimator and least squares estimator for drift parameters of nonlinear reflected stochastic differential equations based on continuous observations. Under some regular conditions, we obtain the consistency and…

We study a class of nonlinear nonparametric inverse problems. Specifically, we propose a nonparametric estimator of the dynamics of a monotonically increasing trajectory defined on a finite time interval. Under suitable regularity…

This paper studies the minimax rate of nonparametric conditional density estimation under a weighted absolute value loss function in a multivariate setting. We first demonstrate that conditional density estimation is impossible if one only…

We consider non-parametric estimation problems in the presence of dependent data, notably non-parametric regression with random design and non-parametric density estimation. The proposed estimation procedure is based on a dimension…

We consider stochastic control with discretionary stopping for the drift of a diffusion process over an infinite time horizon. The objective is to choose a control process and a stopping time to minimize the expectation of a convex terminal…

We consider the problem of statistical inference for the effective dynamics of multiscale diffusion processes with (at least) two widely separated characteristic time scales. More precisely, we seek to determine parameters in the effective…

We consider a 1-dimensional diffusion process X with jumps. The particularity of this model relies in the jumps which are driven by a multidimensional Hawkes process denoted N. This article is dedicated to the study of a nonparametric…

The global estimation problem of the drift function is considered for a large class of ergodic diffusion processes. The unknown drift $S(\cdot)$ is supposed to belong to a nonparametric class of smooth functions of order $k\geq1$, but the…

We investigate a data-driven approach to constructing uncertainty sets for robust optimization problems, where the uncertain problem parameters are modeled as random variables whose joint probability distribution is not known. Relying only…

Nonparametric density estimation is an unsupervised learning problem. In this work we propose a two-step procedure that casts the density estimation problem in the first step into a supervised regression problem. The advantage is that we…

We study the problem of parameter estimation using maximum likelihood for fast/slow systems of stochastic differential equations. Our aim is to shed light on the problem of model/data mismatch at small scales. We consider two classes of…

We study Bayes procedures for the problem of nonparametric drift estimation for one-dimensional, ergodic diffusion models from discrete-time, low-frequency data. We give conditions for posterior consistency and verify these conditions for…

Ordinary differential equations (ODEs), via their induced flow maps, provide a powerful framework to parameterize invertible transformations for the purpose of representing complex probability distributions. While such models have achieved…

We consider the problem of the estimation of the invariant distribution function of an ergodic diffusion process when the drift coefficient is unknown. The empirical distribution function is a natural estimator which is unbiased, uniformly…