Adaptive Drift Estimation for Nonparametric Diffusion Model
نویسندگان
چکیده
We consider a nonparametric diffusion process whose drift and diffusion coefficients are nonparametric functions of the state variable. The goal is to estimate the unknown drift coefficient. We apply a locally linear smoother with a data-driven bandwidth choice. The procedure is fully adaptive and nearly optimal up to a log log factor. The results about the quality of estimation are nonasymptotic and do not require any ergodic or mixing properties of the observed process.
منابع مشابه
Sharp Adaptive Estimation of the Drift Function for Ergodic Diffusions
The global estimation problem of the drift function is considered for a large class of ergodic diffusion processes. The unknown drift S(·) is supposed to belong to a nonparametric class of smooth functions of order k ≥ 1, but the value of k is not known to the statistician. A fully data-driven procedure of estimating the drift function is proposed, using the estimated risk minimization method. ...
متن کاملNonparametric Estimation of Diffusion Processes with Discrete Observations
This paper makes three contributions to the literature on the nonparametric estimation of diffusion processes. First, we show that the nonparametric estimator of the drift function proposed by Stanton (J. of Finance, 1997) is not consistent. Second, we show that a proposed alternative nonparametric estimator of the drift function converges to the true drift in probability, in addition to provid...
متن کاملEquivalence for nonparametric drift estimation of a diffusion process and its Euler scheme
The main goal of the asymptotic equivalence theory of Le Cam (1986) is to approximate general statistical models by simple ones. We develop here a global asymptotic equivalence result for nonparametric drift estimation of a discretely observed diffusion process and its Euler scheme. The asymptotic equivalences are established by constructing explicit equivalence mappings. The impact of such asy...
متن کاملEstimation in Two Classes of Semiparametric Diffusion Models∗
In this paper we propose an estimation method for two classes of semiparametric scalar diffusion models driven by a Brownian motion: In the first class, only the diffusion term is parameterised while the drift is unspecified; in the second, the drift term is specified while the diffusion is of unknown form. The estimation method is based on the assumption of stationarity of the observed process...
متن کاملNonparametric model reconstruction for stochastic differential equations from discretely observed time-series data.
A scheme is developed for estimating state-dependent drift and diffusion coefficients in a stochastic differential equation from time-series data. The scheme does not require to specify parametric forms for the drift and diffusion coefficients in advance. In order to perform the nonparametric estimation, a maximum likelihood method is combined with a concept based on a kernel density estimation...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2000