Partial Ridge-Type Spectral Decomposition Estimate in Linear Mixed Model

As to the linear model with its random effect being common balance multiple classification, Wang and Yin\ucite1 introduced a new parameter estimation method called the spectral decomposition estimate (SDE). In this paper, we generalize the SDE into the situation when the design matrix is ill-conditioned and propose the partial ridge-type spectral decomposition estimate. Through the model transformation of dimensionality reduction which is similar to the principal component estimate, we can easily get that the new estimate has stronger noise-rejection ability and some other important properties. Furthermore, the results we get in the paper can also be easily used in Panel model.