Related papers: On the almost sure convergence of adaptive allocat…
We prove the quasi-optimal convergence of a standard adaptive finite element method (AFEM) for nonlinear elliptic second-order equations of monotone type. The adaptive algorithm is based on residual-type a posteriori error estimators and…
In the setting of multi-armed trials, adaptive designs are a popular way to increase estimation efficiency, identify optimal treatments, or maximize rewards to individuals. Recent work has considered the case of estimating the effects of K…
This paper presents adaptive boundary element methods for positive, negative, as well as zero order operator equations, together with proofs that they converge at certain rates. The convergence rates are quasi-optimal in a certain sense…
The treatment assignment mechanism in a randomized clinical trial can be optimized for statistical efficiency within a specified class of randomization mechanisms. Optimal designs of this type have been characterized in terms of the…
This paper focuses on the estimation of distributional treatment effects in randomized experiments that use covariate-adaptive randomization (CAR). These include designs such as Efron's biased-coin design and stratified block randomization,…
We describe a new family of coupling designs, extending the basic principle of stratified randomization to experiments with continuous, constrained multivariate, text/image and other irregular treatment spaces. Our approach is to first…
In the experimental design literature, Neyman allocation refers to the practice of allocating units into treated and control groups, potentially in unequal numbers proportional to their respective standard deviations, with the objective of…
Optimizing the allocation of units into treatment groups can help researchers improve the precision of causal estimators and decrease costs when running factorial experiments. However, existing optimal allocation results typically assume a…
Response-adaptive allocation designs refer to a class of designs where the probability an observation is assigned to a treatment is changed throughout an experiment based on the accrued responses. Such procedures result in random treatment…
For a homogenization problem associated to a linear elliptic operator, we prove the existence of a distributional corrector and we find an approximation scheme for the homogenized coefficients. We also study the convergence rates in the…
The Robbins-Monro stochastic approximation algorithm is a foundation of many algorithmic frameworks for reinforcement learning (RL), and often an efficient approach to solving (or approximating the solution to) complex optimal control…
We develop two adaptive discretization algorithms for convex semi-infinite optimization, which terminate after finitely many iterations at approximate solutions of arbitrary precision. In particular, they terminate at a feasible point of…
Suppose that we intend to perform an experiment consisting of a set of independent trials. The mean value of the response of each trial is assumed to be equal to the sum of the effect of the treatment selected for the trial, and some…
The comparison of different medical treatments from observational studies or across different clinical studies is often biased by confounding factors such as systematic differences in patient demographics or in the inclusion criteria for…
We consider the procedure proposed by Bhandari et al. (2009) in the context of two-treatment clinical trials, with the objective of minimizing the applications of the less effective drug to the least number of patients. Our focus is on an…
Given n experiment subjects with potentially heterogeneous covariates and two possible treatments, namely active treatment and control, this paper addresses the fundamental question of determining the optimal accuracy in estimating the…
We consider adaptive finite element methods for second-order elliptic PDEs, where the arising discrete systems are not solved exactly. For contractive iterative solvers, we formulate an adaptive algorithm which monitors and steers the…
Emerging applications increasingly demand flexible covariate adaptive randomization (CAR) methods that support unequal targeted allocation ratios. While existing procedures can achieve covariate balance, they often suffer from the shift…
We consider the performance of the difference-in-means estimator in a two-arm randomized experiment under common experimental endpoints such as continuous (regression), incidence, proportion and survival. We examine performance under both…
Matching is a widely used causal inference design that aims to approximate a randomized experiment using observational data by forming matched sets of treated and control units based on similarities in their covariates. Ideally, treated…