What does this research mean for the field?

A novel block-coordinate ascent-like algorithm enables efficient likelihood-based inference for multivariate linear regressions with separable correlation matrices and unrestricted variances, outperforming general-purpose solvers in speed and alternative estimators in accuracy. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To develop computationally efficient likelihood-based estimation and inference methods for multivariate linear regression models featuring separable correlation matrices with unrestricted variances.

August 23, 2026StatOpen Access

Likelihood‐Based Inference With Separable Correlation Matrices

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Authors

KEKarl Oskar Ekvall

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Overview

Methodological study demonstrates efficient likelihood estimation with separable correlation structures, improving accuracy and practical bootstrap testing in complex multivariate data.

Key Points

To develop computationally efficient likelihood-based estimation and inference methods for multivariate linear regression models featuring separable correlation matrices with unrestricted variances.
Designed a block-coordinate ascent algorithm featuring closed-form updates that strictly and monotonically increases likelihood at each iteration until convergence.
Derived standard errors via expected Fisher information computed using Kronecker product properties and implemented parametric bootstrap tests of separability.
Evaluated computational speed and estimator accuracy across numerical simulations and applied the method to dissolved oxygen data from the Mississippi River.
The proposed algorithm converged orders of magnitude faster than general-purpose numerical optimization solvers, making parametric bootstrap testing computationally practical.
Simulations demonstrated lower estimation error compared to both separable covariance and unrestricted estimators, while bootstrap tests maintained nominal size where asymptotic tests failed.
Application to river water data showed that separable correlation models capture site-specific variance heterogeneities that standard separable covariance models fail to detect.

Cite This Study

Karl Oskar Ekvall (2026) studied this question.

synapsesocial.com/papers/6a8aad167677a3411444545f https://doi.org/10.1002/sta4.70174

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August 23, 2026StatOpen Access

Likelihood‐Based Inference With Separable Correlation Matrices

View Full Paper

Ask AI

Bookmark

Authors

KEKarl Oskar Ekvall

Discussion

Member takes

Overview

Methodological study demonstrates efficient likelihood estimation with separable correlation structures, improving accuracy and practical bootstrap testing in complex multivariate data.

Key Points

To develop computationally efficient likelihood-based estimation and inference methods for multivariate linear regression models featuring separable correlation matrices with unrestricted variances.
Designed a block-coordinate ascent algorithm featuring closed-form updates that strictly and monotonically increases likelihood at each iteration until convergence.
Derived standard errors via expected Fisher information computed using Kronecker product properties and implemented parametric bootstrap tests of separability.
Evaluated computational speed and estimator accuracy across numerical simulations and applied the method to dissolved oxygen data from the Mississippi River.
The proposed algorithm converged orders of magnitude faster than general-purpose numerical optimization solvers, making parametric bootstrap testing computationally practical.
Simulations demonstrated lower estimation error compared to both separable covariance and unrestricted estimators, while bootstrap tests maintained nominal size where asymptotic tests failed.
Application to river water data showed that separable correlation models capture site-specific variance heterogeneities that standard separable covariance models fail to detect.

Cite This Study

Karl Oskar Ekvall (2026) studied this question.

synapsesocial.com/papers/6a8aad167677a3411444545f https://doi.org/10.1002/sta4.70174

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