Nearest Neighbour Ratio Imputation with Incomplete Multinomial Outcome in Survey Sampling

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 Any views expressed here are those of the authors and not those of the U.S. Census Bureau. The Census Bureau has reviewed this data product for unauthorized disclosure of confidential information and has approved the disclosure avoidance practices applied (Approval ID: CBDRB-FY21-ESMD002-032).