# High-dimensional Index Volatility Models via Stein's Identity

arXiv: https://arxiv.org/abs/1811.10790 · HTML: https://mlsanity.com/paper/1811.10790/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Nov 2018.

## Built on by (most cited first, 3 of 3)

- [Personalized Federated Learning: A Unified Framework and Universal Optimization Techniques](https://mlsanity.com/paper/2102.09743/) (2021)
- [An Adaptive Stochastic Sequential Quadratic Programming with Differentiable Exact Augmented Lagrangians](https://mlsanity.com/paper/2102.05320/) (2021)
- [Statistical Inference of Constrained Stochastic Optimization via Sketched Sequential Quadratic Programming](https://mlsanity.com/paper/2205.13687/) (2022)

## Abstract (arXiv)

We study the estimation of the parametric components of single and multiple index volatility models. Using the first- and second-order Stein's identities, we develop methods that are applicable for the estimation of the variance index in the high-dimensional setting requiring finite moment condition, which allows for heavy-tailed data. Our approach complements the existing literature in the low-dimensional setting, while relaxing the conditions on estimation, and provides a novel approach in the high-dimensional setting. We prove that the statistical rate of convergence of our variance index estimators consists of a parametric rate and a nonparametric rate, where the latter appears from the estimation of the mean link function. However, under standard assumptions, the parametric rate dominates the rate of convergence and our results match the minimax optimal rate for the mean index estimation. Simulation results illustrate finite sample properties of our methodology and back our theoretical conclusions.