Stationary Jackknife

Author:

Zhou Weilian1,Lahiri Soumendra2ORCID

Affiliation:

1. Department of Statistics North Carolina State University Raleigh NC USA

2. Department of Mathematics and Statistics Washington University St. Louis MO USA

Abstract

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.

Funder

National Science Foundation

Publisher

Wiley

Subject

Applied Mathematics,Statistics, Probability and Uncertainty,Statistics and Probability

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