Two-Step Residual-Based Estimation of Error Variances for Generalized Least Squares in Split-Plot Experiments

Abstract

In split-plot experiments, estimation of unknown parameters by generalized least squares (GLS), as opposed to ordinary least squares (OLS), is required, owing to the existence of whole- and subplot errors. However, estimating the error variances is often necessary for GLS. Restricted maximum likelihood (REML) is an established method for estimating the error variances, and its benefits have been highlighted in many previous studies. This article proposes a new two-step residual-based approach for estimating error variances. Results of numerical simulations indicate that the proposed method performs sufficiently well to be considered as a suitable alternative to REML.

Keywords:

• Generalized least squares
• Response Surface Methodology
• Restricted maximum likelihood
• Split-plot experiment

Mathematics Subject Classification:

• 62K10
• 62K20
• 62J05

Acknowledgments

The authors would like to thank the anonymous reviewers for their valuable comments and suggestions, which greatly improved the manuscript.