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Title - Inference on Time Series Nonparametric Conditional Moment Restrictions Using General Sieves
Abstract - 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.
Bio - Xiaohong Chen is the Malcolm K. Brachman Professor of Economics, Yale University. Previously Chen has taught at University of Chicago, London School of Economics and New York University. Chen got her PhD in Economics from University of California, San Diego.
Chen is an elected member of the American Academy of Arts and Sciences since 2019, a fellow of the Econometric Society since 2007, a founding fellow of the International Association for Applied Econometrics since 2018, a fellow of the Journal of Econometrics since 2012, and an international fellow of Cemmap since 2007. Chen is a winner of the 2017 China Economics Prize. Chen has been a keynote or an invited speaker in many international conferences. She was the 2018 Sargan Lecturer of the Econometric Society, the 2019 Hilda Geiringer Lecturer, and the 2017 Econometric Theory lecturer.
Chen’s research field is econometrics. She is known for her research in penalized sieve estimation and inference on semiparametric and nonparametric models, such as semiparametric models of nonlinear time series, empirical asset pricing, copula, missing data, measurement error, nonparametric instrumental variables, semi/nonparametric conditional moment restrictions, causal inference.
Chen has published peer-reviewed papers in top-ranked general-purpose journals in economics: Econometrica and Review of Economic Studies; as well as in top-ranked journals in statistics and engineering: Annals of Statistics, Journal of the American Statistical Association, IEEE Tran Information Theory, IEEE Trans Neural Networks.
Chen also published several invited review chapters, including a chapter on the method of sieves in 2007 Handbook of Econometrics volumne 6B. She also won Econometric Theory Multa Scripsit Award in 2012, The Journal of Nonparametric Statistics 2010 Best Paper Award, The Richard Stone Prize in Journal of Applied Econometrics for the years 2008 and 2009, The Arnold Zellner Award for the best theory paper published in Journal of Econometrics in 2006 and 2007. Her PhD thesis was about stochastic approximation/Robbins-Monro procedure in function space for near-epoch dependent processes.
Chen is an editor of Journal of Econometrics since Jan 2019.
Chen was an associate editor of Econometrica, Review of Economic Studies, Quantitative Economics, Journal of Econometrics, Econometric Theory, Journal of Nonparametric Statistics, Econometrics Journal, and others.