Fractional Brownian motion: a maximum-likelihood estimator for blurred data

1992 ◽  
Author(s):  
Rachid Harba ◽  
William J. Ohley ◽  
Stephan Hoefer
Keyword(s):  
Brownian Motion ◽  
Maximum Likelihood ◽  
Fractional Brownian Motion ◽  
Maximum Likelihood Estimator ◽  
Likelihood Estimator

Large deviations and Berry–Esseen inequalities for estimators in nonhomogeneous diffusion driven by fractional Brownian motion

2020 ◽  
Vol 28 (3) ◽  
pp. 183-196
Author(s):  
Kouacou Tanoh ◽  
Modeste N’zi ◽  
Armel Fabrice Yodé
Keyword(s):  
Differential Equation ◽  
Brownian Motion ◽  
Maximum Likelihood ◽  
Large Deviations ◽  
Stochastic Differential Equation ◽  
Fractional Brownian Motion ◽  
Maximum Likelihood Estimator ◽  
Bayes Estimator ◽  
Likelihood Estimator

AbstractWe are interested in bounds on the large deviations probability and Berry–Esseen type inequalities for maximum likelihood estimator and Bayes estimator of the parameter appearing linearly in the drift of nonhomogeneous stochastic differential equation driven by fractional Brownian motion.

scholarly journals The Outperformance Probability of Mutual Funds

2019 ◽  
Vol 12 (3) ◽  
pp. 108 ◽  
Author(s):  
Gabriel Frahm ◽  
Ferdinand Huber
Keyword(s):  
Brownian Motion ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Mutual Funds ◽  
Performance Measure ◽  
Money Market ◽  
Statistical Properties ◽  
Likelihood Estimator ◽  
The Given ◽  
Differential Returns

We propose the outperformance probability as a new performance measure, which can be used in order to compare a strategy with a specified benchmark, and develop the basic statistical properties of its maximum-likelihood estimator in a Brownian-motion framework. The given results are used to investigate the question of whether mutual funds are able to beat the S&P 500 or the Russell 1000. Most mutual funds that are taken into consideration are, in fact, able to beat the market. We argue that one should refer to differential returns when comparing a strategy with a given benchmark and not compare both the strategy and the benchmark with the money-market account. This explains why mutual funds often appear to underperform the market, but this conclusion is fallacious.

scholarly journals On Drift Parameter Estimation in Models with Fractional Brownian Motion by Discrete Observations

2014 ◽  
Vol 43 (3) ◽  
pp. 218-228 ◽  
Author(s):  
Yuliya Mishura ◽  
Kostiantyn Ralchenko
Keyword(s):  
Parameter Estimation ◽  
Brownian Motion ◽  
Maximum Likelihood ◽  
Fractional Brownian Motion ◽  
Strong Consistency ◽  
Discrete Observations ◽  
Likelihood Estimator ◽  
True Value ◽  
Differen Tial Equation ◽  
Drift Parameter

We study a problem of an unknown drift parameter estimation in a stochastic differen- tial equation driven by fractional Brownian motion. We represent the likelihood ratio as a function of the observable process. The form of this representation is in general rather complicated. However, in the simplest case it can be simplified and we can discretize it to establish the a. s. convergence of the discretized version of maximum likelihood estimator to the true value of parameter. We also investigate a non-standard estimator of the drift parameter showing further its strong consistency. 

The Comparison Between the Bayes Estimator and the Maximum Likelihood Estimator of the Reliability Function for Negative Exponential Distribution

2018 ◽  
pp. 439
Author(s):  
Hazim Mansour Gorgees ◽  
Bushra Abdualrasool Ali ◽  
Raghad Ibrahim Kathum
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Exponential Distribution ◽  
Reliability Function ◽  
Bayes Estimator ◽  
Likelihood Estimator ◽  
Monte Carlo Simulation Technique ◽  
Negative Exponential Distribution ◽  
Negative Exponential ◽  
Better Than

     In this paper, the maximum likelihood estimator and the Bayes estimator of the reliability function for negative exponential distribution has been derived, then a Monte –Carlo simulation technique was employed to compare the performance of such estimators. The integral mean square error (IMSE) was used as a criterion for this comparison. The simulation results displayed that the Bayes estimator performed better than the maximum likelihood estimator for different samples sizes.

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