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A varying coefficients single-index regression model with responses missing at random is considered. Rank-based estimators of the index coefficient and the functional coefficients are studied, and their asymptotic properties (consistency and asymptotic normality) are established under mild conditions. To demonstrate the performance of the proposed approach, Monte Carlo simulation experiments are carried out and show that the proposed approach provides robust and more efficient estimators compared to its least-squares counterpart. This is demonstrated under different model error structures, including the standard normal, the  t  and the contaminated model error distributions. Finally, a real data example is given to illustrate our proposed method.

Varying coefficient single-index regression model with missing responses under rank-based modelling