Type: Seminar

Distribution: World

Expiry: 8 Jun 2012

Auth: uri@purix (assumed)

John Robinson School of Mathematics and Statistics University of Sydney Location: Carslaw 273 Time: 2pm Friday, Jun 8, 2012 Title: Relative Error of the Bootstrap for Serial Correlation Abstract: Consider the first serial correlation coefficient under an AR(1) model where errors are not assumed to be Gaussian. In this case it is in general necessary to consider bootstrap approximations for tests based on the statistic when the distribution of observations 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.