Nearest Neighbour Ratio Imputation with Incomplete Multinomial Outcome in Survey Sampling

Abstract

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.