This paper presents an estimation method for the random effect parameters and the variance components in linear mixed models. These models may be orthogonal or nonorthogonal. In particular, least squares estimators and the corresponding confidence regions, based on the estimation of quantiles, are considered. As to the random effects parameters, it is only assumed that they have null mean vectors and distributions with known dispersion parameters and second order moments. So, it is not necessary that they are normally distributed. A numerical example considering the normal and the gamma distributions is included, where a comparison with the analysis of variance and a Bayesian estimation based method is provided.

中文翻译：

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非正交混合模型中的推理

本文提出了一种线性混合模型中随机效应参数和方差分量的估计方法。这些模型可以是正交的或非正交的。特别是，考虑基于分位数估计的最小二乘估计量和相应的置信区域。至于随机效应参数，仅假设它们具有零均值向量和分布，具有已知的色散参数和二阶矩。因此，它们不一定是正态分布的。包括考虑正态分布和伽马分布的数值示例，其中提供了与方差分析和基于贝叶斯估计的方法的比较。