Symmetric and Trimmed Solutions of Simple Linear Regression

Least trimmed squares (LTS), as a robust method, is widely used in linear regression models. However, the ordinary LTS of simple linear regression treats the response and prediction variable asymmetrically. In other world, it only considers the errors from response variable. This treatment is not appropriate in some applications. To overcome these problems, we develop three versions of symmetric and trimmed solutions that take into consideration errors from both response and predictor variable. In the thesis, we describe the algorithms to achieve the exact solutions for these three symmetric LTS. We show that these methods lead to more sensible solutions than ordinary LTS. We also apply one of the methods to the microarray normalization problem. It turns out that our LTS based normalization method has advantages over other available normalization methods for microarray data set with large differentiation fractions.