Robust MAVE for single-index varying-coefficient models

In this paper, a robust, efficient and easily implemented estimation procedure for single-index varying-coefficient models is proposed by combining minimum average variance estimation (MAVE) with exponential squared loss. The merit of the proposed method is robust against outliers or heavy-tailed error distributions while asymptotically efficient as the original MAVE under the normal error case. A practical minorization–maximization algorithm is proposed for implementation. Under some regularity conditions, asymptotic distributions of the resulting estimators are derived. Simulation studies and a real data example are conducted to examine the finite sample performance of the proposed method. Both theoretical and empirical findings confirm that our proposed method works very well.