This paper has been discussed two special linear models in two different chapters, one is linear mixed model, the other is linear model with mixed coefficients, and it has been respectively given some results on spectral decomposition estimation of parameter in linear mixed models with heteroscedastic variances and parameter estimation in a linear model with mixed coefficients. First , a spectral composition estimation of the fixed effects and variance components in linear mixed models with heteroscedastic variances, mostly, is done by the methods of matrix transformation and sane corresponding statistic properties of the spectral decomposition estimation is discussed The prominent character of the new estimator is that the estimator of fixed effects is a linear estimation with good statistic properties. Linear mixed models are extensively applied to the fields of economy, finance and mechanical measure, and the estimator acquired by the new method has good statistical and practical purpose. Last, for the problem of estimating parameters, under quadratic loss and matrix loss, in a linear model with mixed coefficients, It has been given that there exist the necessary and sufficient conditions of the uniformly minimum risk unbias (UMRU) estimators and the uniformly minimum risk equi variant (IMRE) estimators of regression coefficients under an aff ine group of transformations , and the necessary and sufficient conditions of the LMRE estimators under a transitive group of transformations respectively. Adnissibility is derived for the general least square (GLS) estimators of regression coefficients. Linear mixed models are important in the fields of economic analysis, reliability singular analysis and biology etc. It is very necessary and significant to research the model, whether from theory or application.
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