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.

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