Stochastic approximation method for kernel sliced average variance estimation

In this paper, we use the stochastic approximation method to estimate Sliced Average Variance Estimation (SAVE). This method is known for its efficiency in recursive estimation. Stochastic approximation is particularly effective for constructing recursive estimators and has been widely used in density estimation, regression, and semi-parametric models. We prove that the resulting estimator is asymptotically normal and root $n$ consistent. Through simulations conducted in the laboratory and applied to real data, we show that it is faster than the kernel method previously proposed. Mathematics subject classification 2020: 62H12; 62J02; 62E20; 62G05.