Abstract: In this study, we aim to reduce the dimension of predictors by considering the central quantile subspace or central subspace. To do so, we use two metrics, the quantile martingale difference divergence and the quantile martingale difference divergence matrix, which measure the quantile dependence of a scalar response variable and a vector of predictors. The proposed dimension-reduction methods do not involve user-chosen parameters and do not assume a parametric model, making them simple to implement. Extensive simulations and a real-data illustration are provided to demonstrate the usefulness of the proposed methods, which are shown to yield competitive finite-sample performance. Theoretical properties are also provided.

Key words and phrases: Central subspace, dimension reduction, quantile dependence.