Nearest neighbor ratio imputation with incomplete multi-nomial outcome in survey sampling

TL;DR

This paper develops a ratio-based nearest neighbor imputation method for handling incomplete multinomial survey data, providing valid variance estimation even with substantial sampling fractions, demonstrated through empirical US survey data.

Contribution

It introduces a novel ratio imputation estimator using auxiliary variables and derives a valid variance estimator accounting for large sampling fractions.

Findings

Proposed estimator performs well in simulations.

Variance estimator remains accurate with non-negligible sampling fractions.

Method effectively estimates detailed expenditure items.

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 neighbor imputation method is used to handle such incomplete multinomial data. In this article, we investigate the nearest neighbor ratio imputation 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 nearest neighbor ratio imputation as a special case of predictive matching imputation and apply the linearization method of \cite{yang2020asymptotic}. 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.