RELATIVE ERRORS FOR BOOTSTRAP APPROXIMATIONS OF THE SERIAL CORRELATION COEFFICIENT

• 成果类型: Article
• 署名作者: Field, Chris; Robinson, John
• 署名单位: Dalhousie University; University of Sydney
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/13-AOS1111
• 发表日期: 2013
• 页码: 1035-1053
• 关键词: saddlepoint approximation; edgeworth

摘要

We consider the first serial correlation coefficient under an AR(1) model where errors are not assumed to be Gaussian. In this case it is necessary to consider bootstrap approximations for tests based on the statistic since the distribution of errors is unknown. We obtain saddle-point approximations for tail probabilities of the statistic and its bootstrap version and use these to show that the bootstrap tail probabilities approximate the true values with given relative errors, thus extending the classical results of Daniels [Biometrika 43 (1956) 169-185] for the Gaussian case. The methods require conditioning on the set of odd numbered observations and suggest a conditional bootstrap which we show has similar relative error properties.