Asymptotics of minimum distance estimator of the parameter of stochastic process driven by a fractional Brownian motion

2008 ◽  
Vol 16 (4) ◽  
Author(s):  
Louis Kouame ◽  
Modeste N'Zi ◽  
Armel Fabrice Yode
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Minimum Distance ◽  
Minimum Distance Estimator ◽  
Distance Estimator

scholarly journals Parameter Estimation for Stochastic Differential Equations Driven by Mixed Fractional Brownian Motion

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Na Song ◽  
Zaiming Liu
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Fractional Brownian Motion ◽  
Asymptotic Properties ◽  
Regularity Conditions ◽  
Minimum Distance Estimator ◽  
Mixed Fractional Brownian Motion ◽  
Distance Estimator ◽  
Drift Parameter

We study the asymptotic properties of minimum distance estimator of drift parameter for a class of nonlinear scalar stochastic differential equations driven by mixed fractional Brownian motion. The consistency and limit distribution of this estimator are established as the diffusion coefficient tends to zero under some regularity conditions.

scholarly journals Asymptotic Distribution of Cramer-von Mises Statistic When Contamination Exists

2015 ◽  
Vol 5 (1) ◽  
pp. 90
Author(s):  
Mayumi Naka ◽  
Ritei Shibata
Keyword(s):  
Maximum Likelihood ◽  
Asymptotic Distribution ◽  
Minimum Distance ◽  
Goodness Of Fit ◽  
Likelihood Estimator ◽  
Goodness Of Fit Test ◽  
Minimum Distance Estimator ◽  
Von Mises Statistic ◽  
Von Mises ◽  
Distance Estimator

In this paper, asymptotic distribution of Cram\'er-von Mises goodness-of-fit test statistic is investigated when contamination exists.<br />We first derive the asymptotic distribution of the Cram\'er-von Mises statistic when the observations are contaminated with noise as a mixture.<br />The result is extended to the case where the parameters are estimated by the minimum distance estimator,<br />which minimizes the Cram\'er-von Mises statistic.<br />In both cases the asymptotic distribution of the Cram\'er-von Mises statistic is given by that of the weighted infinite sum of non-central $\chi^2_1$ variables and the effect of contamination appears only in the non-centrality of the variables.<br />We also demonstrate the robustness of the goodness-of-fit test by Monte Carlo simulations when the parameters are estimated<br />by the minimum distance estimator and the maximum likelihood estimator.<br />Numerical experiments indicate that the use of the minimum distance estimator makes the test insensitive to contamination whereas the power is retained almost the same as that of the maximum likelihood estimator.

scholarly journals On some statistics of fractional Brownian motion

2021 ◽  
pp. 131-138
Author(s):  
Viktor Bondarenko
Keyword(s):  
Stochastic Process ◽  
Time Series ◽  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Hurst Exponent ◽  
Limit Theorems ◽  
Goodness Of Fit ◽  
Mean Square ◽  
One Step ◽  
Optimal Forecasting

Fractional Brownian motion as a method for estimating the parameters of a stochastic process by variance and one-step increment covariance is proposed and substantiated. The root-mean-square consistency of the constructed estimates has been proven. The obtained results complement and generalize the consequences of limit theorems for fractional Brownian motion, that have been proved in the number of articles. The necessity to estimate the variance is caused by the absence of a base unit of time and the estimation of the covariance allows one to determine the Hurst exponent. The established results let the known limit theorems to be used to construct goodness-of-fit criteria for the hypothesis “the observed time series is a transformation of fractional Brownian motion” and to estimate the error of optimal forecasting for time series.

Sign in / Sign up

Export Citation Format

Share Document