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 symmetri...

However, little attention has been devoted to studying multivariate measurements. In particular, we have yet to develop tools to study relationships between measurements. Consider the following examples Example 1.1. Suppose you want to study the relationship between the height of a boy and his father. Here, we take two measurements per child, the child’s height and his/her father’s height, and ...