# Inference on Time Series Nonparametric Conditional Moment Restrictions Using General Sieves

arXiv: https://arxiv.org/abs/2301.00092 · HTML: https://mlsanity.com/paper/2301.00092/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 46 references that are in the map.
- First posted on arXiv 31 Dec 2022.

## Builds on (most cited first, 17 of 17)

- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [Safe, Multi-Agent, Reinforcement Learning for Autonomous Driving](https://mlsanity.com/paper/1610.03295/) (2016)
- [A Theory of Regularized Markov Decision Processes](https://mlsanity.com/paper/1901.11275/) (2019)
- [A Theoretical Analysis of Deep Q-Learning](https://mlsanity.com/paper/1901.00137/) (2019)
- [Why does deep and cheap learning work so well?](https://mlsanity.com/paper/1608.08225/) (2016)
- [Minimax Estimation of Conditional Moment Models](https://mlsanity.com/paper/2006.07201/) (2020)
- [Statistical Inference of the Value Function for Reinforcement Learning in Infinite Horizon Settings](https://mlsanity.com/paper/2001.04515/) (2020)
- [Neural Network Approximation: Three Hidden Layers Are Enough](https://mlsanity.com/paper/2010.14075/) (2020)
- [The power of deeper networks for expressing natural functions](https://mlsanity.com/paper/1705.05502/) (2017)
- [Adversarial Estimation of Riesz Representers](https://mlsanity.com/paper/2101.00009/) (2020)
- [On Well-posedness and Minimax Optimal Rates of Nonparametric Q-function Estimation in Off-policy Evaluation](https://mlsanity.com/paper/2201.06169/) (2022)
- [On the Approximation Power of Two-Layer Networks of Random ReLUs](https://mlsanity.com/paper/2102.02336/) (2021)
- [Optimal policy evaluation using kernel-based temporal difference methods](https://mlsanity.com/paper/2109.12002/) (2021)
- [Learning Functions: When Is Deep Better Than Shallow](https://mlsanity.com/paper/1603.00988/) (2016)
- [An L2 Analysis of Reinforcement Learning in High Dimensions with Kernel and Neural Network Approximation](https://mlsanity.com/paper/2104.07794/) (2021)
- [Deep Learning Statistical Arbitrage](https://mlsanity.com/paper/2106.04028/) (2021)
- [Efficient Estimation in NPIV Models: A Comparison of Various Neural Networks-Based Estimators](https://mlsanity.com/paper/2110.06763/) (2021)

## Built on by (most cited first, 1 of 1)

- [High Dimensional Time Series Regression Models: Applications to Statistical Learning Methods](https://mlsanity.com/paper/2308.16192/) (2023)

## Abstract (arXiv)

General nonlinear sieve learnings are classes of nonlinear sieves that can approximate nonlinear functions of high dimensional variables much more flexibly than various linear sieves (or series). This paper considers general nonlinear sieve quasi-likelihood ratio (GN-QLR) based inference on expectation functionals of time series data, where the functionals of interest are based on some nonparametric function that satisfy conditional moment restrictions and are learned using multilayer neural networks. While the asymptotic normality of the estimated functionals depends on some unknown Riesz representer of the functional space, we show that the optimally weighted GN-QLR statistic is asymptotically Chi-square distributed, regardless whether the expectation functional is regular (root-n estimable) or not. This holds when the data are weakly dependent beta-mixing condition. We apply our method to the off-policy evaluation in reinforcement learning, by formulating the Bellman equation into the conditional moment restriction framework, so that we can make inference about the state-specific value functional using the proposed GN-QLR method with time series data. In addition, estimating the averaged partial means and averaged partial derivatives of nonparametric instrumental variables and quantile IV models are also presented as leading examples. Finally, a Monte Carlo study shows the finite sample performance of the procedure