School of Statistics, East China Normal University, Shanghai, People's Republic of China; Department of Statistics, University of Wisconsin, Madison, WI, USA
School of Statistics and Data Science & LPMC, Nankai University, Tianjin, People's Republic of China
lwangstat@nankai.edu.cn
ABSTRACT
A popular imputation method used to compensate for item nonresponse in sample surveys is the nearest neighbour imputation (NNI) method utilising a covariate to defined neighbours. When the covariate is multivariate, however, NNI suffers the well-known curse of dimensionality and gives unstable results. As a remedy, we propose a single-index NNI when the conditional mean of response given covariates follows a single index model. For estimating the population mean or quantiles, we establish the consistency and asymptotic normality of the single-index NNI estimators. Some limited simulation results are presented to examine the finite-sample performance of the proposed estimator of population mean.