A Class Of Liu-type Estimator And Its Superiorities

The research about least square estimation of regression parameters in the linear model has included integrated and systemic results. But the multicollinearity problem cause the least squares estimation is not accuracy, so biased estimate stepped onto the historical stage, and one of a class of biased estimation is LIU estimation.In this paper, we study a class of special LIU-type estimation’s optimal property, and we define such LIU-type estimation as SLE estimation. The author analyses its linearity, property of biased estimation, estimation of compressibility, admissible estimation, and researchs its superiority under the rules of Residual Sum of Squares (RSS for short), Mean Square Error Matrix (MSEM for short) and Balance Loss Function (BLF for short) based on the SLE estimation. This paper also has attempted to get a kind of method to calculate the two parameters of SLE estimation.This paper introduces the history of the development, research background and status about general linear model and biased estimation in the first part. The Chapter2introduces the knowledge of matrix theory and the definitions of ridge estimation, Stein estimation and LIU estimation, as well as several lemma and theorem. Some properties of the SLE estimation are studied in the Chapter3; this chapter proves the SLE estimation is a kind of admissible estimation, analyzes the improvement conditions of SLE estimation is better than LSE estimation and Ridge estimation under the rules of the Residual Sum of Squares, Mean Square Error Matrix and Balance Loss Function, and obtains the corresponding conclusions. The fourth chapter discusses the method to select parameter of SLE estimation, and presents a case to analyze the superiority of SLE estimation and least squares estimate under the rule of balance risk loss function. The last chapter is the paper’s conclusions and prospects for the future. There are two figure, three table, and twenty-five references in this paper.