Abstract: The limiting distribution for M-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 the M-estimate. In this paper, we show that the bootstrap procedure is asymptotically valid for a class of M-estimates provided the bootstrap resample size Mn satisfies mn→∞ and mn/n→ 0 as the original sample size n goes to infinity.
Key words and phrases: Autoregressive processes, bootstrap, M-estimation, Poisson processes, regular variation, stable laws.