Bootstrapping robust regression

Abstract

In the last chapter we have made extensive use of the simple (linear) structure of the model and of the estimate. As an example of a more complicated estimator we study in this chapter bootstrap of M-estimates $\hat \beta$in linear models. As in the last chapter for each n we consider the linear model

$$ \begin{array}{*{20}{c}} {{Y_i} = X_i^T\beta + {\varepsilon _i}}&{\left( {i = 1, \ldots ,n} \right)} \end{array} $$

(1.1)

where the X_i’s and β are p-dimensional vectors, the Y_i’s are the observations and the ε _i’s are i.i.d. errors distributed according to a distribution P. The X_i’s and p may depend on n (see the discussion of this point in the last chapter). The content of this chapter is also contained in Mammen(1989a).