Bootstrap Inference for a First-Order Autoregression with Positive Innovations
研究了正创新一阶自回归模型中自回归参数的极值估计量，提出Bootstrap方法构造完全非参数的置信区间，并用于偏差校正，通过模拟和实例验证。
Abstract In this article we consider statistical inference for the autoregressive parameter of a first-order autoregressive sequence with positive innovations via an extreme value estimator ϕ. We show that a bootstrap procedure correctly estimates the sampling distribution of an asymptotically pivotal quantity (whose distribution depends only on the exponent of regular variation of the innovation distribution) based on ϕ, provided that the ratio of the bootstrap sample size m and the original sample size n converges to zero. This result enables us to construct a totally nonparametric confidence interval for the autoregressive parameter. We also consider bootstrapping a normalized version of ϕ with an application toward bias correction. To obtain the bootstrap validity results, we develop a continuous convergence result for certain associated point processes. We also present results of simulation studies and a numerical example.