Bootstrapping M-estimates in regression and autoregression with infinite variance. Statistica Sinica 7

Abstract: The limiting distribution forM-estimates in a regression or autoregression model with heavy-tailed noise is generally intractable, which precludes its use for inference purposes. Alternatively, the bootstrap can be used to approximate the sampling distribution of theM-estimate. In this paper, we show that the bootstrap procedure is asymptotically valid for a class ofM-estimates provided the bootstrap resample size mn satisfies mn → ∞ and mn/n → 0 as the original sample size n goes to infinity