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Abstract:
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In the context of imputed survey data, Mashreghi, Léger and Haziza (2014) proposed a rescaling bootstrap method for the case of stratified simple random sampling without replacement with uniform nonresponse in each stratum. Their method consists of selecting bootstrap samples according to the Rao and Wu (1988) rescaling bootstrap method and then regenerating nonresponse within each bootstrap sample using independent Bernoulli trials with the observed response rate. Afterwards, the nonrespondents in the bootstrap sample are reimputed using the same imputation method that was used on the original data. In this work, a new bootstrap method under the rescaling bootstrap approach is proposed to handle unequal response probabilities. Under this method, a novel technique is applied to rescale the imputed survey data through solving certain systems of linear equations. In this bootstrap procedure, after taking bootstrap samples from the set of rescaled values, bootstrap response indicators are generated using the estimated response probabilities. A simulation study shows the great performance of the proposed method in terms of relative bias and coverage probability.
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