Stochastic approximation method for kernel sliced average variance estimation

TL;DR

This paper introduces a stochastic approximation approach for kernel sliced average variance estimation, providing a faster recursive estimator that is asymptotically normal and root n consistent, with demonstrated efficiency in simulations and real data.

Contribution

It presents a novel stochastic approximation method for SAVE that improves computational speed and maintains statistical properties, advancing recursive estimation techniques.

Findings

Estimator is asymptotically normal

Estimator is root n consistent

Faster than previous kernel methods

Abstract

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.