Improved Rates and Asymptotic Normality for Nonparametric Neural Network Estimators

By Xiaohong Chen, Halbert White. 1999

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Deep Neural Networks for Estimation and Inference: Application to Causal Effects and Other Semiparametric Estimands (2018, background): “, 2011, 2012; Farrell, 2015) and tree/forest based methods (Wager and Athey, 2018), though earlier work studied shallow (typically with a single hidden layer) neural networks with smooth activation functions (White, 1989, 1992; Chen and White, 1999).”
Double/Debiased Machine Learning for Treatment and Causal Parameters (2016, background): “election in sparse models; Luo and Spindler (2016) for L 2-boosting in sparse linear models; Wager and Walther (2016) for concentration results for a class of regression trees and random forests; and Chen and White (1999) for a class of neural nets. However, the presented conditions allow for more r”
Chapter 76 Large Sample Sieve Estimation of Semi-Nonparametric Models (2007, background): “We now present a result of Chen and Shen (1996) for i.i.d. data; see Chen and Shen (1998) for the stationary beta-mixing case and Chen and White (1999) for the stationary uniform-mixing case.”
Implementing Nonparametric and Semiparametric Estimators (2006, background): “For this class of functions, Chen and White (1999) constructs an estimator which converges in mean square with rate (n/ lnn)−(1+2/(d+1))/[4(1+1/(d+1))] .”
Estimation of possibly misspecified semiparametric conditional moment restriction models with different conditioning variables (2007, methodology): “For commonly used nonlinear sieves An such as neural network and ridgelet nonlinear sieves, we have ln[N(δ,An, || · ||s)] = ckhn ln(khnδ ) [see e.g. Chen and White (1999)], hence Assumption 3.7(i) is satisfied as long as khn ln(khn)/n → 0.”
Efficient Estimation of Models with Conditional Moment Restrictions Containing Unknown Functions (2003, background): “…be found in econometrics applications such as Fenton and Gallant (1996) for Hermite polynomials, Newey (1997) for spline and power series, Chen, Hansen and Scheinkman (1997) for shape-preserving wavelet B-spline with unbounded support, and Chen and White (1999) for multivariate neural networks.”
DEEP NEURAL NETWORKS FOR ESTIMATION AND INFERENCE (2020, background): “In that time, shallow neural networks with smooth activation functions were shown to have many good theoretical properties (White (1992), Anthony and Bartlett (1999), Chen and White (1999)).”
Double/debiased machine learning for treatment and structural parameters (2017, unknown): “Within this setting, there is a large classical literature focused on low-dimensional settings that provides methods for adjusting for confounding variables including regression methods, propensity score adjustment methods, matching methods, and “doubly-robust” combinations of these methods; see, fo”
Artificial intelligence as structural estimation: Deep Blue, Bonanza, and AlphaGo (2017, background): “, the states with only five pieces, and all possible future states that can be reached from them), as well as selected six-piece positions.(7) (7)A database with all five-piece endings requires 7.”