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Fiducial intervals for variance components in an unbalanced two-component normal mixed linear model. (English) Zbl 1471.62410

Summary: We propose a new method for constructing confidence intervals for \(\sigma_{\alpha}^2,\sigma^2_{\varepsilon}\), and the intraclass correlation \(\rho =\sigma_{\alpha}^2(\sigma_{\alpha}^2+\sigma_{\epsilon}^2)\) in a two-component mixed-effects linear model. This method is based on an extension of R. A. Fisher’s fiducial argument. We conducted a simulation study to compare the resulting interval estimates with other competing confidence interval procedures from the literature. Our results demonstrate that the proposed fiducial intervals have satisfactory performance in terms of coverage probability, as well as shorter average confidence interval lengths overall. We also prove that these fiducial intervals have asymptotically exact frequentist coverage probability. The computations for the proposed procedures are illustrated using real data examples.

MSC:

62J05 Linear regression; mixed models
62F25 Parametric tolerance and confidence regions
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