Confidence intervals for marginal parameters under imputation for item nonresponse

Abstract

Item nonresponse occurs frequently in sample surveys and other approaches to data collection. We consider three different methods of imputation to fill in the missing values in a random sample { Y i , i = 1 , … , n } : (i) mean imputation ( M), (ii) random hot deck imputation ( R), and (iii) adjusted random hot deck imputation ( A). Asymptotic normality of the imputed estimators of the mean μ under M, R and A and the distribution function θ = F ( y ) and qth quantile θ q , under R and A is established, assuming that the values are missing completely at random. This result is used to obtain normal approximation (NA)-based confidence intervals on μ , θ and θ q . In the case of θ q , Woodruff [1952. Confidence intervals for medians and other position measures, J. Amer. Statist. Assoc. 47, 635–646]-type confidence intervals are also obtained under R and A. Empirical log-likelihood ratios for the three cases are also obtained and shown to be asymptotically scaled χ 1 2 . This result is used to obtain asymptotically correct empirical likelihood (EL)-based confidence intervals on μ , θ and θ q . Results of a simulation study on the finite sample performance of NA-based and EL-based confidence intervals are reported. Confidence intervals obtained here do not require identification flags on the imputed values in the data file; only the estimated response rate is needed with the imputed data file. This feature of our method is important because identification flags often may not be provided in practice with the data file due to confidentiality reasons.