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.

Maximum-likelihood estimation in non-standard conditions

1971 ◽  
Vol 70 (3) ◽  
pp. 441-450 ◽  
Author(s):  
P. A. P. Moran
Keyword(s):  
Maximum Likelihood ◽  
Parameter Space ◽  
Null Hypothesis ◽  
Maximum Likelihood Estimators ◽  
Likelihood Estimation ◽  
Standard Theory ◽  
True Parameter ◽  
Open Set ◽  
Estimation Problems ◽  
Parameter Point

The origin of the present paper is the desire to study the asymptotic behaviour of certain tests of significance which can be based on maximum-likelihood estimators. The standard theory of such problems (e.g. Wald(4)) assumes, sometimes tacitly, that the parameter point corresponding to the null hypothesis lies inside an open set in the parameter space. Here we wish to study what happens when the true parameter point, in estimation problems, lies on the boundary of 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 Nonlinear Split-Plot Design Model in Parameters Estimation using Estimated Generalized Least Square - Maximum Likelihood Estimation

2018 ◽  
Vol 9 (2) ◽  
pp. 65
Author(s):  
Ikwuoche John David ◽  
Osebekwin Ebenenzer Asiribo ◽  
Hussain Garba Dikko
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Variance Components ◽  
Likelihood Estimation ◽  
Parameters Estimation ◽  
Least Square ◽  
Design Model ◽  
Mixed Effect ◽  
Split Plot ◽  
Plot Design

This research aimed to provide a theoretical framework for intrinsically nonlinear models with two additive error terms. To achieve this, an iterative Gauss-Newton via Taylor Series expansion procedures for Estimated Generalized Least Square (EGLS) technique was adopted. This technique was applied in estimating the parameters of an intrinsically nonlinear split-plot design model where the variance components were unknown. The unknown variance components were estimated via Maximum Likelihood Estimation (MLE) method. To achieve the numerical stability in the iterative process of estimating the parameters, Householder QR decomposition was used. The results show that EGLS method presented in this research is available and applicable to estimate linear fixed, random, and mixed-effect models. However, in practical situations, the functional form of the mean in the model is often nonlinear due to the dynamics involved in the system process.

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