We study the principal components of covariance estimators in multivariate mixed-effects linear models. show that, high dimensions, eigenvalues and eigenvectors may exhibit bias aliasing effects that are not present low-dimensional settings. derive first-order limits eigenvalue locations eigenvector projections a high-dimensional asymptotic framework, allowing for general population spectral di...

This paper tries to tell the story of the general linear model, which saw the light of day 200 years ago, and the assumptions underlying it. We distinguish three principal stages (ignoring earlier more isolated instances). The model was first proposed in the context of astronomical and geodesic observations, where the main source of variation was observational error. This was the main use of th...

This paper considers the heteroscedastic multivariate linear model with errors following elliptically contoured distributions. The marginal likelihood function of the unknown covariance parameters and the predictive distribution of future responses have been derived. The predictive distribution obtained is a product of m multivariate Student’s t distributions. It is interesting to note that whe...

We consider linear models where d potential causes X1, . . . , Xd are correlated with one target quantity Y and propose a method to infer whether the association is causal or whether it is an artifact caused by overfitting or hidden common causes. We employ the idea that in the former case the vector of regression coefficients has ‘generic’ orientation relative to the covariance matrix ΣXX of X...

Assuming a general linear model with unknown and possibly unequal normal error variances, the interest is to develop a one-sample procedure to handle the statistical problems involving point estimation, confidence region, and general linear hypotheses on regression parameters. The sampling procedure is to split up each single sample of size ni at a controllable regressor’s data point into two p...

This paper presents the basic concepts of stability in fuzzy linguistic models. Theauthors have proposed a criterion for BIBO stability analysis of fuzzy linguistic modelsassociated to linear time invariant systems [25]-[28]. This paper presents the basic concepts ofstability in the general nonlinear and linear systems. This stability analysis method is verifiedusing a benchmark system analysis.

Linear mixed models are able to handle an extraordinary range of complications in regression-type analyses. Their most common use is to account for within-subject correlation in longitudinal data analysis. They are also the standard vehicle for smoothing spatial count data. However, when treated in full generality, mixed models can also handle spline-type smoothing and closely approximate krigi...