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Nearest neighbour ratio imputation with incomplete multinomial outcome in survey sampling

Author

Listed:
  • Chenyin Gao
  • Katherine Jenny Thompson
  • Jae Kwang Kim
  • Shu Yang

Abstract

Nonresponse is a common problem in survey sampling. Appropriate treatment can be challenging, especially when dealing with detailed breakdowns of totals. Often, the nearest neighbour imputation method is used to handle such incomplete multinomial data. In this article, we investigate the nearest neighbour ratio imputation (NNRI) estimator, in which auxiliary variables are used to identify the closest donor and the vector of proportions from the donor is applied to the total of the recipient to implement ratio imputation. To estimate the asymptotic variance, we first treat the NNRI as a special case of predictive matching imputation and build on earlier work to linearize the imputed estimate. To account for the non‐negligible sampling fractions, parametric and generalized additive models are employed to incorporate the smoothness of the imputation estimator, which results in a valid variance estimator. We apply the proposed method to estimate expenditures detail items based on empirical data from the 2018 collection of the Service Annual Survey, conducted by the United States Census Bureau. Our simulation results demonstrate the validity of our proposed estimators and also confirm that the derived variance estimators have good performance even when the sampling fraction is non‐negligible.

Suggested Citation

  • Chenyin Gao & Katherine Jenny Thompson & Jae Kwang Kim & Shu Yang, 2022. "Nearest neighbour ratio imputation with incomplete multinomial outcome in survey sampling," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(4), pages 1903-1930, October.
    • Handle: RePEc:bla:jorssa:v:185:y:2022:i:4:p:1903-1930
    DOI: 10.1111/rssa.12841
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    References listed on IDEAS

    as
    1. Shu Yang & Jae Kwang Kim, 2020. "Asymptotic theory and inference of predictive mean matching imputation using a superpopulation model framework," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(3), pages 839-861, September.
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    8. Shu Yang & Jae Kwang Kim, 2019. "Nearest Neighbor Imputation for General Parameter Estimation in Survey Sampling," Advances in Econometrics, in: The Econometrics of Complex Survey Data, volume 39, pages 209-234, Emerald Group Publishing Limited.
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