Semiparametric fractional imputation using empirical likelihood in survey sampling

Area of Science:

• Statistics
• Survey Methodology

Background:

• Item nonresponse is a significant challenge in survey sampling, potentially biasing results.
• Traditional imputation methods often rely on strong parametric assumptions.
• Empirical likelihood offers a flexible framework for statistical inference.

Purpose of the Study:

• To propose a novel semiparametric fractional imputation method using empirical likelihood to handle item nonresponse.
• To avoid parametric model assumptions required by existing methods.
• To provide a robust approach for obtaining consistent estimates in the presence of nonresponse.

Main Methods:

• Utilizing the empirical likelihood method to derive fractional weights based on observed residuals.
• Applying a regression model for the first moment condition, without assuming its full parametric form.
• Employing a jackknife method for variance estimation.

Main Results:

• The proposed semiparametric fractional imputation method yields [Formula: see text]-consistent estimates for parameters.
• The method effectively handles item nonresponse by leveraging empirical likelihood.
• Simulation studies demonstrate the performance of the new imputation estimator compared to others.

Conclusions:

• The empirical likelihood-based fractional imputation is a viable and robust alternative for handling item nonresponse in surveys.
• This semiparametric approach offers advantages by relaxing model assumptions.
• The method provides a statistically sound basis for inference with incomplete survey data.