My research focuses on adaptive experimental design, sequential experimentation, adaptive sampling, and statistical inference. I develop efficient statistical methods for allocation and decision-making in experiments, with applications in clinical trials and biomedical research..
Adaptive Sampling and Allocation
I study adaptive sampling and allocation strategies that use information accumulated during an experiment to guide future sampling decisions. A particular focus is understanding the theoretical behavior of these allocation rules and their convergence to meaningful oracle allocations.
Adaptive Experimental Design
I explore sequential approaches to experimental design where the optimal allocation depends on unknown model parameters. The goal is to develop efficient allocation strategies that adapt to accumulating information while maintaining reliable statistical inference.
Adaptive Clinical Trials
I am interested in statistical methodology for adaptive clinical trials, including response-adaptive randomization and related allocation strategies, with an emphasis on efficient experimentation and reliable inference.
Project 1: D-Optimal Designs & PICS
D-optimal designs maximize the determinant of the Fisher information matrix. For nonlinear models, the Fisher information depends on unknown parameters, so sequential designs optimize the D-optimality criterion using current estimates, updating via maximum likelihood. The PICS (Plug into Closed-form Solution) strategy replaces repeated optimization with draws from the distribution induced by the known optimal design using current estimates. Simulations show higher efficiency, and asymptotic normality of the estimators is established.
Project 2: Causal Inference under Adaptive Treatment Assignment
Adaptive treatment assignment introduces dependence that invalidates classical inference. We study estimation of the Average Treatment Effect using IPW and AIPW estimators in a finite-population framework. We introduce design stability to characterize long-run behavior of assignment probabilities and establish asymptotic normality and valid variance estimation under this condition. The framework applies to common adaptive randomization schemes such as Wei’s and Efron’s designs, enabling valid inference in adaptive experiments.
Project 3: Estimation under Adaptive Data
Adaptive data collection can distort OLS estimation, inflating errors and breaking asymptotic normality. We study how adaptivity affects estimation of low-dimensional parameters in high-dimensional linear models. OLS or centered-OLS can achieve near-i.i.d. error under certain conditions. We also propose the TALE (Two-stage Adaptive Linear Estimating equation) for single-coordinate inference, proving asymptotic normality under weak adaptivity.