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Adjusted Jackknife for Imputation under Unequal Probability Sampling without Replacement

Yves G. Berger and J. N. K. Rao
Journal of the Royal Statistical Society. Series B (Statistical Methodology)
Vol. 68, No. 3 (2006), pp. 531-547
Published by: Wiley for the Royal Statistical Society
Stable URL: http://www.jstor.org/stable/3879290
Page Count: 17
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Adjusted Jackknife for Imputation under Unequal Probability Sampling without Replacement
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Abstract

Imputation is commonly used to compensate for item non-response in sample surveys. If we treat the imputed values as if they are true values, and then compute the variance estimates by using standard methods, such as the jackknife, we can seriously underestimate the true variances. We propose a modified jackknife variance estimator which is defined for any without-replacement unequal probability sampling design in the presence of imputation and non-negligible sampling fraction. Mean, ratio and random-imputation methods will be considered. The practical advantage of the method proposed is its breadth of applicability.

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