scholarly journals Exact maximum likelihood estimator for drift fractional Brownian motion at discrete observation

2011 ◽  
Vol 31 (5) ◽  
pp. 1851-1859 ◽  
Author(s):  
Hu Yaozhong ◽  
Nualart David ◽  
Xiao Weilin ◽  
Zhang Weiguo
Keyword(s):  
Brownian Motion ◽  
Maximum Likelihood ◽  
Fractional Brownian Motion ◽  
Maximum Likelihood Estimator ◽  
Likelihood Estimator ◽  
Discrete Observation ◽  
Exact Maximum Likelihood

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.

Shape averages and their Bias

1994 ◽  
Vol 26 (2) ◽  
pp. 334-340 ◽  
Author(s):  
K. V. Mardia ◽  
I. L. Dryden
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Simulation Study ◽  
Normal Model ◽  
Likelihood Estimator ◽  
Distributional Properties ◽  
Exact Maximum Likelihood

The paper considers the bias of Bookstein's mean estimator for shape under the isotropic normal model. This work depends on certain distributional properties of shape variables. An alternative unbiased modified estimator is proposed and its performance is compared with various estimators, including Procrustes and the exact maximum likelihood estimator, in a simulation study.

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.

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