A (Partially) Model-Based Look at Jackknife Variance Estimation with Two-Phase Samples
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This paper focuses on a design-consistent regression estimator in which the “auxiliaries” are
estimated from a stratified cluster sample and the regression coefficients from an arbitrary
subsample of the original sample. The reweighted expansion estimator described in Stukel
and Kott (1997) is an example of such an estimator. Assuming that the target variable is a
linear function of the auxiliaries plus an error term, asymptotic properties for both this
estimator and the jackknife estimator of its mean squared error are developed. These
theoretical results are used to explain some of Stukel and Kott’s empirical findings, which
in turn shed light on the asymptotic underpinnings of the theoretical results.