Computing the LTS estimator: Why is it almost surely the case that the k 1 k 1 matrix X*, with rows selected

Computing the LTS estimator: Why is it almost surely the case that the

ðk þ 1Þ · ðk þ 1Þ matrix X*, with rows selected from among those of the complete model matrix X, is of full rank when all its rows are different? (Put another way, how is it possible that X* would not be of full rank?) Thinking in terms of the ðk þ 1Þ-dimensional scatterplot of Y against X1; ... ; Xk , what does the hyperplane defined by b* ¼ X*%1y* represent?