Fast and robust bootstrap for LTS

The Least Trimmed Squares (LTS) estimator is a frequently used robust estimator of regression. When it comes to inference for the parameters of the regression model, the asymptotic normality of the LTS estimator can be used. However, this is usually not appropriate in situations where the use of robust estimators is recommended. The bootstrap method constitutes an alternative, but has two major drawbacks. First, since the LTS in itself is a computer-intensive estimator, the classical bootstrap can be extremely time-consuming. And second, the breakdown point of the procedure is lower than that of the estimator itself. To overcome these problems, an alternative bootstrap method is proposed which is both computationally simple and robust. In each bootstrap sample, instead of recalculating the LTS estimates, an approximation is computed using information from the LTS solution in the original sample. A simulation study shows that this method performs well, particularly regarding confidence intervals for the regression parameters. An example is given to illustrate the benefits of the method.