Correcting Jackknife Confidence Intervals

This paper presents a method for constructing confidence intervals using the jackknife. Asymptotic expansions are used to assess and reduce the skewness. It is proved that, although the error in the coverage rate remains of order O(1/n) for two-sided intervals, the main term due to the skewness in the distribution is eliminated, which constitute an improvement to the normal approximation that is important in the context of small samples. Several simulations are presented, with different distributions and functionals, and compared to the empirical accuracy obtained with a normal approximation. It is observed that our method produces in many cases a better empirical accuracy than the intervals due to a normal approximation, without requiring any knowledge on the underlying distribution.