Asymptotics with increasing dimension for robust regression with applications to the bootstrap

A stochastic expansion for MM-estimates in linear models with many parameters is derived under the weak condition κn1/3(logn)2/3→0κn1/3(log⁡n)2/3→0, where nn is the sample size and κκ the maximal diagonal element of the hat matrix. The expansion is used to study the asymptotic distribution of linear contrasts and the consistency of the bootstrap. In particular, it turns out that bootstrap works in cases where the usual asymptotic approach fails.