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 demonstrate 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.

翻译：本文采用随机逼近方法估计切片平均方差估计（SAVE）。该方法以递归估计的高效性著称，特别适用于构建递归估计器，并已广泛应用于密度估计、回归分析和半参数模型。我们证明了所得估计量具有渐近正态性和根n相合性。通过实验室模拟和实际数据应用，我们证明该方法比先前提出的核方法具有更快的计算速度。