Nearest neighbor ratio imputation with incomplete multinomial outcome in survey sampling

Area of Science:

• Statistics
• Survey Methodology

Background:

• Survey nonresponse is a pervasive challenge, particularly for detailed data analysis.
• Nearest neighbor imputation is a common technique for handling incomplete multinomial survey data.

Purpose of the Study:

• To investigate a novel nearest neighbor ratio imputation estimator.
• To develop a valid variance estimator that accounts for non-negligible sampling fractions.

Main Methods:

• The nearest neighbor ratio imputation method was investigated using auxiliary variables.
• Linearization methods (Yang and Kim, 2020) were applied to estimate asymptotic variance.
• Parametric and generalized additive models were employed to incorporate imputation estimator smoothness.

Main Results:

• The proposed nearest neighbor ratio imputation estimator demonstrated validity in simulations.
• The derived variance estimators performed well, even with substantial sampling fractions.
• The method was successfully applied to estimate expenditure details from the 2018 Service Annual Survey.

Conclusions:

• The nearest neighbor ratio imputation estimator offers a robust approach for survey data with nonresponse.
• The developed variance estimation techniques provide reliable results under various sampling conditions.
• This methodology enhances the accuracy of detailed expenditure estimations in large-scale surveys.