scholarly journals Maximum Likelihood Estimation in the Fractional Vasicek Model

2017 ◽  
Vol 56 (1) ◽  
pp. 77-87 ◽  
Author(s):  
Stanislav Lohvinenko ◽  
Kostiantyn Ralchenko
Keyword(s):  
Brownian Motion ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Asymptotic Normality ◽  
Maximum Likelihood Estimators ◽  
Likelihood Estimation ◽  
Hurst Parameter ◽  
Unknown Parameters ◽  
Vasicek Model ◽  
Consistency And Asymptotic Normality

We consider the fractional Vasicek model of the form dXt = (α-βXt)dt +γdBHt , driven by fractional Brownian motion BH with Hurst parameter H ∈ (1/2,1). We construct the maximum likelihood estimators for unknown parameters α and β, and prove their consistency and asymptotic normality.

Maximum likelihood estimation for sub-fractional Vasicek model

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
B. L. S. Prakasa Rao
Keyword(s):  
Brownian Motion ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Fractional Brownian Motion ◽  
Asymptotic Properties ◽  
Maximum Likelihood Estimators ◽  
Likelihood Estimation ◽  
Vasicek Model ◽  
Model Driven

Abstract We investigate the asymptotic properties of maximum likelihood estimators of the drift parameters for the fractional Vasicek model driven by a sub-fractional Brownian motion.

scholarly journals New class of Lindley distributions: properties and applications

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Duha Hamed ◽  
Ahmad Alzaghal
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Simulation Study ◽  
Likelihood Estimation ◽  
Statistical Properties ◽  
Data Sets ◽  
Lifetime Data ◽  
Unknown Parameters ◽  
Lindley Distribution ◽  
New Class

AbstractA new generalized class of Lindley distribution is introduced in this paper. This new class is called the T-Lindley{Y} class of distributions, and it is generated by using the quantile functions of uniform, exponential, Weibull, log-logistic, logistic and Cauchy distributions. The statistical properties including the modes, moments and Shannon’s entropy are discussed. Three new generalized Lindley distributions are investigated in more details. For estimating the unknown parameters, the maximum likelihood estimation has been used and a simulation study was carried out. Lastly, the usefulness of this new proposed class in fitting lifetime data is illustrated using four different data sets. In the application section, the strength of members of the T-Lindley{Y} class in modeling both unimodal as well as bimodal data sets is presented. A member of the T-Lindley{Y} class of distributions outperformed other known distributions in modeling unimodal and bimodal lifetime data sets.

scholarly journals On estimation in multilevel models with block circular symmetric covariance structure

2012 ◽  
Vol 16 (1) ◽  
pp. 83-96
Author(s):  
Yuli Liang ◽  
Dietrich von Rosen ◽  
Tatjana von Rosen
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Parameter Space ◽  
Variance Components ◽  
Multilevel Model ◽  
Multilevel Models ◽  
Covariance Structure ◽  
Maximum Likelihood Estimators ◽  
Likelihood Estimation

In this article we consider a multilevel model with block circular symmetric covariance structure. Maximum likelihood estimation of the parameters of this model is discussed. We show that explicit maximum likelihood estimators of variance components exist under certain restrictions on the parameter space.

scholarly journals Scalable Bias-corrected Linkage Disequilibrium Estimation Under Genotype Uncertainty

2021 ◽  
Author(s):  
David Gerard
Keyword(s):  
Linkage Disequilibrium ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Maximum Likelihood Estimators ◽  
Likelihood Estimation ◽  
Real Data ◽  
Standard Errors ◽  
Posterior Distributions ◽  
Posterior Mean ◽  
Genome Wide

AbstractLinkage disequilibrium (LD) estimates are often calculated genome-wide for use in many tasks, such as SNP pruning and LD decay estimation. However, in the presence of genotype uncertainty, naive approaches to calculating LD have extreme attenuation biases, incorrectly suggesting that SNPs are less dependent than in reality. These biases are particularly strong in polyploid organisms, which often exhibit greater levels of genotype uncertainty than diploids. A principled approach using maximum likelihood estimation with genotype likelihoods can reduce this bias, but is prohibitively slow for genome-wide applications. Here, we present scalable moment-based adjustments to LD estimates based on the marginal posterior distributions of the genotypes. We demonstrate, on both simulated and real data, that these moment-based estimators are as accurate as maximum likelihood estimators, and are almost as fast as naive approaches based only on posterior mean genotypes. This opens up bias-corrected LD estimation to genome-wide applications. Additionally, we provide standard errors for these moment-based estimators. All methods are implemented in the ldsep package on the Comprehensive R Archive Network https://cran.r-project.org/package=ldsep.

scholarly journals Maximum likelihood Estimation for Stochastic Differential Equations with two Random Effects in the Diffusion Coefficient

2016 ◽  
Vol 11 (10) ◽  
pp. 5697-5704
Author(s):  
Mohammed Sari Alsukaini ◽  
Alkreemawi khazaal Walaa ◽  
Wang Xiang Jun
Keyword(s):  
Differential Equation ◽  
Maximum Likelihood ◽  
Random Effects ◽  
Diffusion Coefficients ◽  
Likelihood Function ◽  
Asymptotic Properties ◽  
Likelihood Estimation ◽  
Likelihood Estimator ◽  
Unknown Parameters ◽  
Consistency And Asymptotic Normality

We study n independent stochastic processes(xi (t),tiЄ[o,t1 ],i=1,......n) defined by a stochastic differential equation with diffusion coefficients depending nonlinearly on a random variables  and  (the random effects).The distributions of the random effects Ñ„i,and,μi and  depends on unknown parameters which are to be estimated from the continuous observations of the processes xi (t) . When the distributions of the random effects Ñ„ ,μ, are Gaussian and exponential respectively, we obtained an explicit formula for the likelihood function and the asymptotic properties (consistency and asymptotic normality) of the maximum likelihood estimator (MLE) are derived when  tend to infinity.

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