Statistical Consultants Ltd
Statistical Analysis Techniques, Robust Estimators, Alternatives to OLS
The three main classes of robust estimators are M, L and R. Robust estimators are resistant to outliers and when used in regression modelling, are robust to departures from the normality assumption.
L-estimators involve a linear combination of order statistics. With univariate data, the sample median and α-trimmed mean are examples of L-estimators. In regression, the focus is on the order of residuals.
Least Trimmed of Squares (LTS)The LTS method takes the following steps:
1. Fit an OLS model to the data
2. Store the residuals as its own variable
3. Sort data set by the size of residuals
4. Delete the observations that have the α smallest and α largest residuals, where 0<α<0.5
5. Fit an OLS model to the remaining observations.
The LTS has a breakdown point equal to α. The breakdown point is the percentage of the data that can be outlying before the fitted line is attracted to the outlying points.
Median Squares (
method involves finding the
beta coefficients that minimise the median squared residual. Since the objective function
differentiable, the problem requires an algorithm to solve it.
|Copyright © Statistical Consultants Ltd 2010|