Multiply Robust Bootstrap Variance Estimation in the Presence of Singly Imputed Survey Data

Area of Science:

• Statistics
• Survey Methodology
• Computational Statistics

Background:

• Single imputation is a common method for handling item nonresponse in surveys.
• Treating imputed values as observed data can lead to underestimation of variance.
• Accurate variance estimation is crucial for reliable statistical inference from survey data.

Purpose of the Study:

• To propose novel bootstrap schemes for variance estimation after multiply robust imputation.
• To develop methods that can handle large sampling fractions.
• To provide variance estimators with the multiple robustness property.

Main Methods:

• Development of three pseudo-population bootstrap schemes.
• Application of multiply robust imputation procedures.
• Simulation studies to evaluate performance.

Main Results:

• The proposed bootstrap methods effectively estimate the variance of imputed estimators.
• The methods demonstrate good performance in terms of relative bias and coverage probability.
• The procedures are suitable for large sampling fractions.

Conclusions:

• The proposed pseudo-population bootstrap schemes offer a robust approach to variance estimation in the presence of item nonresponse and imputation.
• These methods improve the accuracy of statistical inference for population totals and quantiles.
• The multiple robustness property enhances the reliability of the estimators.