Combining Some Biased Estimation Methods with Least Trimmed Squares Regression and its Application

Betül Kan-Kilinç,Ozlem Alpu

doi:10.15446/rce.v38n2.51675

Abstract

<p>In the case of multicollinearity and outliers in regression analysis, the researchers are encouraged to deal with two problems simultaneously. Biased methods based on robust estimators are useful for estimating the regression coefficients for such cases. In this study we examine some robust biased estimators on the datasets with outliers in x direction and outliers in both x and y direction from literature by means of the R package ltsbase. Instead of a complete data analysis, robust biased estimators are evaluated using capabilities and features of this package.</p>

Highlights

Peter Rousseeuw introduced several robust estimators including Least Trimmed Squares (LTS) in his works
LTS estimator is defined on an objective function which is minimized by h min (e2)i:n βi=1 where (e2)i:n is the ith smallest residual or distance when the residuals are ordered in ascending order
Rousseeuw & van Driessen (1999) proposed a fast algorithm based on a random sampling for computing LTS which was published as Rousseeuw & van Driessen (2006)

Summary

The Least Trimmed Squares

Least Trimmed Squares (LTS) or Least Trimmed Sum of Squares is one of a number of methods for robust regression (Rousseeuw & Leroy 1987). Peter Rousseeuw introduced several robust estimators including LTS in his works. LTS is a statistical robust technique for fitting a linear regression model to a set of n points given a trimming parameter h as it is insensitive due to outliers (n/2 ≤ h ≤ n). As h is the number of good data points, LTS estimator obtaines a robust estimate by trimming the (n − h) data points having the largest residuals from the data set. Rousseeuw & van Driessen (1999) proposed a fast algorithm based on a random sampling for computing LTS which was published as Rousseeuw & van Driessen (2006). Only the FAST-LTS algorithm proposed by Rousseeuw and van Driessen will be considered. The last section presents the remarkable difference between the ltsbase and previous algorithms in R

Contributions to LTS in the Presence of Multicollinearity

Robust Biased Estimators

The ltsbase Package

Case Study 1

Case Study 2

Conclusions