Bootstrap Inference for a First-Order Autoregression with Positive Innovations
作者:
Somnath Datta,
WilliamP. McCormick,
期刊:
Journal of the American Statistical Association
(Taylor Available online 1995)
卷期:
Volume 90,
issue 432
页码: 1289-1300
ISSN:0162-1459
年代: 1995
DOI:10.1080/01621459.1995.10476633
出版商: Taylor & Francis Group
关键词: Autocorrelation coefficient;Bootstrap;Extreme value estimator;Point processes;Positive AR(1) processes;Regular variation
数据来源: Taylor
摘要:
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 sizemand the original sample sizenconverges 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.
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