多线性混合张量模型及其参数估计

Multilinear mixed effect tensor regression models and their parameter estimations

考察多参数多元统计回归多重线性模型的参数估计问题。首先,建立线性混合模型,并利用向量化方法,结合多元函数的高阶导数和似然估计方法,给出了均值向量和方差的估计;其次,通过张量给出了多线性混合张量模型的表达;最后,利用高阶张量分解给出多线性混合模型中的参数向量的估计。

We investigated multivariate mixed effect regression models and their parameter estimations. We established a linear mixed model with matrix form, and presented an estimation method based on the combination of the vectorization,higher order derivatives and the likelihood estimations. We also built a multilinear mixed effect tensor model and presented estimations for the mean matrix B and the covariances in the model.