Dynamic Robust Bootstrap for Linear Model Selection Using LTS

The Ordinary Least Squares (OLS) method is often use to estimate the parameters of a linear model. Under certain assumptions, the OLS estimates are the best linear unbiased estimates. One of the important assumptions of the linear model is that the error terms are normally distributed. Unfortunately, many researchers are not aware that the performance of the OLS can be very poor when the data set for which one often makes a normal assumption, has a heavy-tailed distribution which may arise as a result of outliers. One way to deal with this problem is to use robust statistics which is less affected by the presence of outliers. Another possibility is to apply a bootstrap technique which does not rely on the normality assumption.In this book the use of bootstrap technique is emphasize. Unfortunately, many statistics practitioners are not aware of the fact that most of the classical bootstrap techniques are based on the OLS estimates which is sensitive to outliers. The problems are further complicated when the percentage of outliers in the bootstrap samples are greater than the percentage of outliers in the original sample.