Bootstrap estimation of covariance matrices via the percentile method

Consistency of the bootstrap second moments does not usually follow from the proofs of consistency of the distribution of the bootstrap. Here it is shown that the convergence of the bootstrap distribution to a normal variate implicitly defines a consistent estimator for the asymptotic second moments. The estimator is based on the L-estimation of the scale parameter of arbitrary linear combinations of the bootstrap sequence and uses Classical Minimum Distance techniques to impose the positive semi-definiteness restrictions. Copyright 2005 Royal Economic Society