Dimension reduction based on conditional multiple index density function

In this paper, a dimension reduction method is proposed by using the first derivative of the conditional density function of response given predictors. To estimate the central subspace, we propose a direct methodology by taking expectation of the product of predictor and kernel function about response, which helps to capture the directions in the conditional density function. The consistency and asymptotic normality of the proposed estimation methodology are investigated. Furthermore, we conduct some simulations to evaluate the performance of our proposed method and compare with existing methods, and a real data set is analyzed for illustration.