Generalized signed-rank estimation for regression models with non-ignorable missing responses

In regression modeling, it has become very common to deal with missing data, which render the statistical analysis more difficult. It is then of interest to develop robust methods toward statistical inference for the regression coefficients in the presence of missing data. From this, a generalized signed-rank estimator of the regression coefficients in a model with non-ignorable missing responses is studied. The generalized signed-rank objective function covers a large class of existing objective functions such as the least squares, the signed-rank, the least absolute deviation among others. Under mild regularity conditions, the consistency and the limiting distribution of the proposed estimator are established. Finite-samples simulation studies are carried out to assess the performance of the proposed estimation method, and a practical real data application is given to illustrate our method. Results of these studies show that the proposed approach results in a robust and more efficient estimator compared to the least squares and least absolute deviation approaches, when dealing with heavy-tailed, contaminated model error distributions and/or when data contain gross outliers in the response space. Under the standard normal model error distribution, while the least squares and the proposed estimator have a similar performance, the least absolute deviation is inefficient.