Confidence intervals for marginal parameters under fractional linear regression imputation for missing data

Abstract

Item nonresponse occurs frequently in sample surveys and other applications. Imputation is commonly used to fill in the missing item values in a random sample { Y i ; i = 1 , … , n } . Fractional linear regression imputation, based on the model Y i = X i ′ β + ν 0 ( X i ) ϵ i with independent zero mean errors ϵ i , is used to create one or more imputed values in the data file for each missing item Y i , where { X i , i = 1 , … , n } , is observed completely. Asymptotic normality of the imputed estimators of the mean μ = E ( Y ) , distribution function θ = F ( y ) for a given y, and qth quantile θ q = F - 1 ( q ) , 0 < q < 1 is established, assuming that Y is missing at random (MAR) given X. This result is used to obtain normal approximation (NA)-based confidence intervals on μ , θ and θ q . In the case of θ q , a Bahadur-type representation and Woodruff-type confidence intervals are also obtained. Empirical likelihood (EL) ratios are also obtained and shown to be asymptotically scaled χ 1 2 variables. This result is used to obtain asymptotically correct 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.