Covariates missing at random under signed-rank inference

A robust regression analysis in the presence of missing covariates is considered. The signed-rank estimator of the regression coefficients is studied, where the missing covariates are imputed under the assumption that they are missing at random. The consistency and asymptotic normality of the proposed estimator are established under mild conditions. Monte Carlo simulation experiments are carried out. They demonstrate that the signed-rank estimator is more efficient than the least squares and the least absolute deviations estimators whenever the error distribution is heavy tailed or contaminated. Under the standard normal model error distribution with well specified conditional distribution of the missing covariates, the least-squares and signed-rank methods provide similar results while the least absolute deviations method is inefficient. Finally, the use of the proposed methodology is illustrated using the economic and political data on nine developing countries in Asia from 1980 to 1999.