Abstract: In this article, we use a Hilbert-Schmidt Independence Criterion to propose a new method for estimating directions in single-index models. This approach enjoys a model free property and requires no link function to be smoothed or estimated. Further, we propose a permutation test to check whether the estimated single-index is sufficient. The sampling distribution of our estimator is established. Finite sample performance of proposed estimates is examined through simulation studies and compared with two well-established methods: the refined Minimum Average Variance Estimation method (rMAVE, Xia et al. (2002)) and the Estimating Function Method (EFM, Cui, Hardle, and Zhu (2011)). A New Zealand Horse Mussels data set is analyzed via our approach to demonstrate the efficacy of our proposed approach.

Key words and phrases: Central subspace, Hilbert-Schmidt independence criterion, permutation test, single-index models, sufficient dimension reduction.