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April 2013 Relative errors for bootstrap approximations of the serial correlation coefficient
Chris Field, John Robinson
Ann. Statist. 41(2): 1035-1053 (April 2013). DOI: 10.1214/13-AOS1111


We consider the first serial correlation coefficient under an $\operatorname{AR}(1)$ 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.


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Chris Field. John Robinson. "Relative errors for bootstrap approximations of the serial correlation coefficient." Ann. Statist. 41 (2) 1035 - 1053, April 2013.


Published: April 2013
First available in Project Euclid: 29 May 2013

zbMATH: 1360.62203
MathSciNet: MR3099130
Digital Object Identifier: 10.1214/13-AOS1111

Primary: 62G09 , 62G10 , 62G20
Secondary: 62M10

Keywords: Autoregression , Saddle-point approximations

Rights: Copyright © 2013 Institute of Mathematical Statistics


Vol.41 • No. 2 • April 2013
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