相关论文: Nadaraya-Watson estimator for reflected stochastic…

We study the nonparametric Nadaraya-Watson estimator of the drift function for ergodic stochastic processes driven by fractional Brownian motion of Hurst parameter H > 1/2. The estimator is based on the discretely observed stochastic…

This paper deals with a nonparametric Nadaraya-Watson estimator $\hat b$ of the drift function computed from independent continuous observations of a diffusion process. Risk bounds on $\hat b$ and its discrete-time approximation are…

This paper deals with a nonparametric Nadaraya-Watson (NW) estimator of the transition density function computed from independent continuous observations of a diffusion process. A risk bound is established on this estimator. The paper also…

This paper deals with the consistency and a rate of convergence for a Nadaraya-Watson estimator of the drift function of a stochastic differential equation driven by an additive fractional noise. The results of this paper are obtained via…

We study the problem of parameter estimation for reflected stochastic processes driven by a standard Brownian motion. The estimator is obtained using nonlinear least squares method based on discretely observed processes. Under some certain…

A non-parametric diffusion model with an additive fractional Brownian motion noise is considered in this work. The drift is a non-parametric function that will be estimated by two methods. On one hand, we propose a locally linear estimator…

Nonstationary high-dimensional time series are increasingly encountered in biomedical research as measurement technologies advance. Owing to the homeostatic nature of physiological systems, such datasets are often located on, or can be well…

We investigate the asymptotic behavior of the Nadaraya-Watson estimator for the estimation of the regression function in a semiparametric regression model. On the one hand, we make use of the recursive version of the sliced inverse…

Bifurcating autoregressive processes, which can be seen as an adaptation of au-toregressive processes for a binary tree structure, have been extensively studied during the last decade in a parametric context. In this work we do not specify…

We consider a class of nonparametric time series regression models in which the regressor takes values in a sequence space. Technical challenges that hampered theoretical advances in these models include the lack of associated Lebesgue…

We investigate nonparametric drift estimation for multidimensional jump diffusions based on continuous observations. The results are derived under anisotropic smoothness assumptions and the estimators' performance is measured in terms of…

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 the asymptotic behavior of estimators of a two-valued, discontinuous diffusion coefficient in a Stochastic Differential Equation, called an Oscillating Brownian Motion. Using the relation of the latter process with the Skew…

This article studies a trimmed version of the Nadaraya-Watson estimator to estimate the unknown non-parametric regression function. The characterization of the estimator through minimization problem is established, and its pointwise…

The nonparametric estimation of integrated diffusion processes has been extensively studied, with most existing research focusing on pointwise convergence. This paper is the first to establish uniform convergence rates for the…

We consider a stochastic differential equation of the form $dr_t = (a - b r_t) dt + \sigma\sqrt{r_t}dW_t$, where $a$, $b$ and $\sigma$ are positive constants. The solution corresponds to the Cox-Ingersoll-Ross process. We study the…

In this paper sequential monitoring schemes to detect nonparametric drifts are studied for the random walk case. The procedure is based on a kernel smoother. As a by-product we obtain the asymptotics of the Nadaraya-Watson estimator and its…

We consider the problem of estimating the roughness of the volatility process in a stochastic volatility model that arises as a nonlinear function of fractional Brownian motion with drift. To this end, we introduce a new estimator that…

In a regression model, we write the Nadaraya-Watson estimator of the regression function as the quotient of two kernel estimators, and propose a bandwidth selection method for both the numerator and the denominator. We prove risk bounds for…

This paper deals with a copies-based continuously differentiable and strictly decreasing estimator of the drift function for stochastic differential equations defining recurrent diffusion processes. The first part of our paper deals with…