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Optimal a priori balance in the design of controlled experiments
Author(s) -
Kallus Nathan
Publication year - 2018
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/rssb.12240
Subject(s) - covariate , minimax , pairwise comparison , a priori and a posteriori , kernel (algebra) , consistency (knowledge bases) , parametric statistics , mathematical optimization , computer science , variance (accounting) , randomized experiment , mathematics , econometrics , statistics , artificial intelligence , accounting , epistemology , combinatorics , business , philosophy
Summary We develop a unified theory of designs for controlled experiments that balance baseline covariates a priori (before treatment and before randomization) using the framework of minimax variance and a new method called kernel allocation. We show that any notion of a priori balance must go hand in hand with a notion of structure, since with no structure on the dependence of outcomes on baseline covariates complete randomization (no special covariate balance) is always minimax optimal. Restricting the structure of dependence, either parametrically or non‐parametrically, gives rise to certain covariate imbalance metrics and optimal designs. This recovers many popular imbalance metrics and designs previously developed ad hoc , including randomized block designs, pairwise‐matched allocation and rerandomization. We develop a new design method called kernel allocation based on the optimal design when structure is expressed by using kernels, which can be parametric or non‐parametric. Relying on modern optimization methods, kernel allocation, which ensures nearly perfect covariate balance without biasing estimates under model misspecification, offers sizable advantages in precision and power as demonstrated in a range of real and synthetic examples. We provide strong theoretical guarantees on variance, consistency and rates of convergence and develop special algorithms for design and hypothesis testing.