Saddlepoint Approximations for the Difference of Order Statistics and Studentized Sample Quantiles
Chunsheng Ma and John Robinson
Research Report 97-36
Date: December 1997
For a sample from a given distribution the difference of two order statistics
and the studentized quantile are statistics whose distribution is needed to
obtain tests and confidence intervals for quantiles and quantile
differences. This paper gives saddlepoint approximations for densities and
saddlepoint approximations of the Lugannani-Rice form for tail probabilities
of these statistics. The relative errors of the approximations are 1/n
uniformly in a neighbourhood of the parameters and this uniformity is global
if the densities are log-concave.
saddlepoint approximation. Laplace method.
difference of order statistics. Studentized sample quantile.
AMS Subject Classification (1991)
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Sydney Mathematics and Statistics