Stationary Jackknife

Variance estimation is an important aspect in statistical inference, especially in the dependent data situations. Resampling methods are ideal for solving this problem since these do not require restrictive distributional assumptions. In this paper, we develop a novel resampling method in the Jackknife family called the stationary jackknife. It can be used to estimate the variance of a statistic in the cases where observations are from a general stationary sequence. Unlike the moving block jackknife, the stationary jackknife computes the jackknife replication by deleting a variable length block and the length has a truncated geometric distribution. Under appropriate assumptions, we can show the stationary jackknife variance estimator is a consistent estimator for the case of the sample mean and, more generally, for a class of nonlinear statistics. Further, the stationary jackknife is shown to provide reasonable variance estimation for a wider range of expected block lengths when compared with the moving block jackknife by simulation.

Automated summary

Variance estimation is crucial in statistical inference, especially when dealing with dependent data. Resampling methods, such as the newly developed stationary jackknife introduced in this paper, offer a solution that does not rely on restrictive distributional assumptions. The stationary jackknife is capable of estimating the variance of a statistic in cases where the observations are derived from a general stationary sequence, and it outperforms the traditional moving block jackknife in providing more reasonable variance estimates across a wider range of expected block lengths, as demonstrated through simulation experiments.