Biased Estimation Of Parameters In A Linear Model Of Mixed Coefficients

The linear model of mixed coefficient is a kind of linear model with both fixed coefficient and random coefficient.It is an important model in statistical model.Parameter estimation is a very important research field in the study of linear model of mixed coefficient.The least squares estimate of the mixed coefficient linear model parameters is the best linear unbiased estimate,but if the linear model of the mixed coefficient has multicollinearity,the least squares estimation property is no longer good.In response to this problem,many scholars have proposed a number of improved methods,and biased estimation is one of the important improvements.In this paper,combined with the existing literature research,three kinds of biased estimates are proposed from three different perspectives,and the properties of these types of estimates are discussed.Firstly,the s-d-K estimation is proposed by combining the Liu estimation with the s-K estimation.The related properties are discussed and the necessary and sufficient conditions for the s-d-K estimation to be better than the least squares estimation,Liu estimation and s-K estimation are given in the sense of the mean square error matrix.The Monte Carlo simulation further validates the superiority of the new estimation.Secondly,almost unbiased Liu estimation is defined by almost unbiased enlightenment.Research shows that under the quadratic deviation criterion,almost unbiased Liu estimation is better than Liu estimation,and sufficient conditions for almost unbiased Liu estimation over least squares estimation and Liu estimation are given in the sense of mean square error.The superiority of the new estimation is further verified by Monte Carlo simulation and case analysis.Finally,almost unbiased s-d-K estimation is proposed by combining the almost unbiased thought with the s-d-K estimation.The research shows that under the quadratic deviation criterion,the almost unbiased s-d-K estimation is better than the s-d-K estimation;In the sense of the mean square error matrix,The almost unbiased s-d-K estimation is superior to the least squares estimation and several types of almost unbiased estimation.The Monte Carlo simulation is used to further verify the superiority of almost unbiased s-d-K estimation.