Nonparametric Methods for Stochastic Systems: Model Calibration and Online Decision-Making

Abstract

Modern stochastic systems, from computer simulations to real-time decision platforms, increasingly rely on flexible statistical methods that can adapt to complex, high-dimensional data without restrictive parametric assumptions. Nonparametric approaches have emerged as powerful tools for such challenges, offering robustness and scalability. This dissertation focuses on two problems in this domain: (1) improving model calibration for imperfect computer simulations, and (2) developing robust and efficient methods for online decision-making with high-dimensional covariates and fairness constraints.

For model calibration of imperfect computer simulations, we propose Sobolev calibration, a flexible nonparametric framework that minimizes discrepancies measured by reproducing kernel Hilbert space (RKHS) norm. Our approach addresses the potential overfitting problem in existing methods while establishing a novel theoretical connection between the classic L₂ calibration and Kennedy-O’Hagan’s calibration. The proposed method achieves fast convergence rate, asymptotic normality, and semiparametric efficiency, and is supported by empirical validation.

Date of Award	2025
Original language	English
Awarding Institution	The Hong Kong University of Science and Technology
Supervisor	Yuan YAO (Supervisor) & Wenjia WANG (Supervisor)