Evaluating the Effective Degrees of Freedom of the Delete-a-Group Jackknife

Abstract

The delete-a-group jackknife is sometimes used when estimating the variances of statistics based on a large sample. We investigate heavily poststratified estimators for a population mean and a simple regression coefficient, where both full-sample and domain estimates are of interest. The delete-a-group (DAG) jackknife employing 30, 60, and 100 replicates is found to be highly unstable, even for large sample sizes. The empirical degrees of freedom of these DAG jackknives are usually much less than their nominal degrees of freedom. This analysis calls into question whether coverage intervals derived from replication-based variance estimators can be trusted for highly calibrated estimates.

Keywords:

• Calibrated weight
• Domain
• Ignorable sample design
• Linearization variance estimator
• Model parameter.

Mathematics Subject Classification:

• Primary 62D05
• Secondary 62G05
• 62G20.

Acknowledgments

Much of this work was performed at the National Agricultural Statistics Service, where Dr. Kott was employed as a research statistician from 1987 until 2009, and where Dr. Garren was employed as a research statistician during the summers of 2007–2009.