What Should Be Done When an Estimated Between-Group Covariance Matrix Is Not Nonnegative Definite?

Amemiya, Yasuo

doi:10.2307/2682808

Cited by 48 publications

(42 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is worthy to note that both of the matrices R G and A Ã are positive definite. When the matrices are not positive definite, the methods as proposed by Amemiya (1985) and Calvin and Dykstra (1991) are able to deal with this issue.…”

Section: Developing Revised P/t Ratiomentioning

confidence: 98%

Determining the optimal allocation of parameters for multivariate measurement system analysis

Pan

2015

Expert Systems with Applications

View full text Add to dashboard Cite

Section: Developing Revised P/t Ratiomentioning

confidence: 98%

Determining the optimal allocation of parameters for multivariate measurement system analysis

Pan

2015

Expert Systems with Applications

View full text Add to dashboard Cite

“…Let q 1 denote the rank of B 1 , and it is noted that q 1 min(q, N − k). Assumed that q 1 < N − k. Then we get the following canonical form: S, 1 and y 2 are mutually independently distributed as…”

Section: Canonical Formsmentioning

confidence: 99%

“…Although the estimation of variance components in univariate mixed linear models have been considered extensively in the literature, the estimation of multivariate components of variance has not been well studied primarily due to technical difficulties. For some explanations on this topic, see Amemiya [1], Calvin and Dykstra [3], Mathew et al [14] and Srivastava and Kubokawa [18]. In the estimation of the 'within' component of variance , in Section 3, we derive general types of truncated estimators improving on the unbiased and/or the James-Stein minimax estimators in the general mixed effects model (1.1).…”

Section: Introductionmentioning

confidence: 99%

Estimation of covariance matrices in fixed and mixed effects linear models

Kubokawa

Tsai

2006

Journal of Multivariate Analysis

View full text Add to dashboard Cite

The estimation of the covariance matrix or the multivariate components of variance is considered in the multivariate linear regression models with effects being fixed or random. In this paper, we propose a new method to show that usual unbiased estimators are improved on by the truncated estimators. The method is based on the Stein-Haff identity, namely the integration by parts in the Wishart distribution, and it allows us to handle the general types of scale-equivariant estimators as well as the general fixed or mixed effects linear models.

show abstract

“…This is a common problem in the estimation of variance components by method of moments. A modified estimator of S proposed by Amemiya (1985), which will be always nonnegative definite isS S 0 ¼Ŝ S 0 ; ifŜ S 0 is nonnegative definite…”

Section: The Starting Valuesmentioning

confidence: 99%

An Approximate EM Algorithm for Nonlinear Mixed Effects Models

Al-Zaid¹,

Yang

2001

Biom. J.

View full text Add to dashboard Cite

In this article, we construct an approximate EM algorithm to estimate the parameters of a nonlinear mixed effects model. The iterative procedure can be viewed as an iterative method of moments procedure for estimating the variance components and an iterative reweighted least squares estimates for estimating the fixed effects. Therefore, it is valid without the normality assumptions on the random components. A computationally simple method of moments estimates of the model parameters are used as the starting values for our iterative procedure. A simulation study was conducted to compare the performances of the proposed procedure with the procedure proposed by Lindstrom and Bates (1990) for some normal models and nonnormal models.

show abstract

What Should Be Done When an Estimated Between-Group Covariance Matrix Is Not Nonnegative Definite?

Cited by 48 publications

References 0 publications

Determining the optimal allocation of parameters for multivariate measurement system analysis

Determining the optimal allocation of parameters for multivariate measurement system analysis

Estimation of covariance matrices in fixed and mixed effects linear models

An Approximate EM Algorithm for Nonlinear Mixed Effects Models

Contact Info

Product

Resources

About