From Nonparametric Density Estimation to Parametric Estimation of Multidimensional Diffusion Processes

Nonparametric Density Estimation via Diffusion Mixing

Suppose we are given empirical data and a prior density about the distribution of the data. We wish to construct a nonparametric density estimator that incorporates the prior information. We propose an estimator that allows for the incorporation of prior information in the density estimation procedure within a non-Bayesian framework. The prior density is mixed with the available empirical data ...

Parametric versus Nonparametric Estimation of Diffusion Processes — A Monte Carlo Comparison

In this paper, a Monte Carlo simulation is performed to investigate the finite sample properties of various estimators, based on discretely sampled observations, of the continuous-time Itô diffusion process. The simulation study aims to compare the performance of the nonparametric estimators proposed in Jiang and Knight (1996) with common parametric estimators based on those diffusion processes...

Sequential nonparametric density estimation

Nonparametric volatility density estimation

B E RT VA N E S , P E T E R S P R E I J 1 and HARRY VAN ZANTEN 2 Korteweg-de Vries Institute for Mathematics, University of Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands. E-mail: [email protected]; [email protected] Division of Mathematics and Computer Science, Faculty of Sciences, Free University Amsterdam, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands...

Nonparametric 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...