[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-118476-en":3,"doc-seo-118476-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},118476,1374391974468,"Eden","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",8,"Research & Report","Machine Learning for Econometrics - Theoretical Foundations and Empirical Insights - Dissertation","Machine learning methods for econometric settings are investigated with a focus on detecting weak signals and evaluating predictive risk. The study develops theoretical results for ridge and lasso predictors, analyzes signal-to-noise and sparsity regimes, and validates findings through Monte Carlo experiments. It further extends the framework using deep autoencoders for nonlinear factor models and recurrent neural networks for time series, combining mathematical proofs with empirical applications across multiple economic datasets.","THE UNIVERSITY OF CHICAGO  \nMACHINE LEARNING FOR ECONOMETRICS: THEORETICAL FOUNDATIONS  \nAND EMPIRICAL INSIGHTS  \nA DISSERTATION SUBMITTED TO  \nTHE FACULTY OF THE UNIVERSITY OF CHICAGO  \nBOOTH SCHOOL OF BUSINESS  \nIN CANDIDACY FOR THE DEGREE OF  \nDOCTOR OF PHILOSOPHY  \nBY  \nZHOUYU SHEN  \nCHICAGO, ILLINOIS  \nJUNE 2025  \nCopyright © 2025 by Zhouyu Shen All Rights Reserved  \nTo everyone who has guided, encouraged, and supported me throughout this journey  \nTABLE OF CONTENTS  \nLIST OF FIGURES .................................... vii  \nLIST OF TABLES ..................................... viii  \nACKNOWLEDGMENTS ................................. ix  \nABSTRACT ........................................ x  \n1 CAN MACHINES LEARN WEAK SIGNALS? ................... 1  \n1.1 Introduction .................................... 1  \n1.2 Theoretical Results ................................ 7  \n1.2.1 Model Setup ................................ 7  \n1.2.2 Predictors ................................. 10  \n1.2.3 Bayes Risk ................................. 11  \n1.2.4 Zero’s Optimality and Relative Prediction Error ............ 14  \n1.2.5 Analysis of the Ridge Predictor ..................... 17  \n1.2.6 Analysis of the Lasso Predictor ..................... 20  \n1.2.7 Assessing Signal-to-Noise Ratio ..................... 23  \n1.2.8 Mixed Signal Strengths and Alternative Benchmarks ......... 24  \n1.2.9 Ridge vs. Lasso in Extremely Sparse Settings ............. 27  \n1.3 Monte Carlo Simulations ............................. 28  \n1.3.1 Ridge and Lasso for Linear Models ................... 28  \n1.3.2 Advanced Machine Learning Methods for Nonlinear Models ...... 30  \n1.4 Empirical Analysis of Six Economic Datasets .................. 34  \n1.4.1 Finance 1: Market Equity Premium ................... 35  \n1.4.2 Finance 2: Cross-Section of Expected Returns ............. 36  \n1.4.3 Macro 1: Macroeconomic Forecasting .................. 36  \n1.4.4 Macro 2: Economic Growth Across Countries ............. 38  \n1.4.5 Micro 1: Crime Rates across US States ................. 39  \n1.4.6 Micro 2: Eminent Domain and Economic Outcomes .......... 40  \n1.5 Conclusion ..................................... 41  \n1.6 Mathematical Proofs ............................... 42  \n1.6.1 Proof of Theorem 1 ............................ 42  \n1.6.2 Proof of Theorem 2 ............................ 43  \n1.6.3 Proof of Theorem 3 ............................ 45  \n1.6.4 Proof of Theorem 4 ............................ 47  \n1.6.5 Proof of Proposition 1 .......................... 48  \n1.6.6 Proof of Theorem 5 ............................ 49  \n1.6.7 Proof of Proposition 2 .......................... 52  \n1.7 Supplemental Simulation Results ........................ 54  \n1.7.1 Additional Simulations with Fixed Tunings ............... 54  \n1.7.2 Out-of-sample R2 ............................. 56  \n1.7.3 Why Lasso Fails? ............................. 57  \n1.7.4 Robustness Check ............................. 58  \n1.8 Choice of Tuning Parameters .......................... 59  \n1.9 Technical Lemmas and Their Proofs ...................... 61  \n2 DEEP AUTOENCODERS FOR NONLINEAR FACTOR MODELS: THEORY AND APPLICATIONS .................................... 98  \n2.1 Introduction .................................... 98  \n2.2 Model Setup .................................... 103  \n2.2.1 Nonlinear Factor Model ......................... 103  \n2.2.2 Autoencoders and Their Architecture .................. 105  \n2.3 Main Theoretical Results ............................. 110  \n2.3.1 Recovery of the Common Components ................. 111  \n2.3.2 Recovery of the Factors .......................... 114  \n2.3.3 Extensions and Applications ....................... 117  \n2.4 Monte Carlo Simulations ............................. 127  \n2.4.1 Simulation Setup ............................. 127  \n2.4.2 Finite-Sample Recovery of Common Components with Autoencoders 129  \n2.4.3 Simulation Comparison with Kernel PCA and Local PCA ...... 132  \n2.4.4 F","cbCaij1xSB0TIHHk","https://ap.wps.com/l/cbCaij1xSB0TIHHk","pdf",5760404,1,270,"English","en",105,"# Table of Contents\n## List of Figures\n## List of Tables\n## Acknowledgments\n## Abstract\n## 1 Can Machines Learn Weak Signals?\n## 2 Deep Autoencoders for Nonlinear Factor Models: Theory and Applications\n## 3 Recurrent Neural Networks Meet Time Series: A Theoretical Perspective\n## References","[{\"question\":\"What problem does the dissertation address in the econometrics context?\",\"answer\":\"It examines whether machine learning can learn weak signals for econometric prediction, analyzing predictive risk and signal-to-noise considerations.\"},{\"question\":\"How are ridge and lasso predictors analyzed?\",\"answer\":\"The dissertation derives theoretical results comparing ridge and lasso, including conditions of optimality and performance in sparse regimes, supported by Monte Carlo simulations.\"},{\"question\":\"Which additional machine learning models extend the main theoretical agenda?\",\"answer\":\"Deep autoencoders are used for nonlinear factor models, and recurrent neural networks are studied for time series, with both theoretical proofs and empirical applications.\"}]","Machine Learning for Econometrics - Theoretical Foundations and Empirical Insights - Dissertation | 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