We study minimax-optimal designs and estimators for estimating the sample average treatment effect in finite population randomized experiments, where both design and estimator are unrestricted. For binary potential outcomes, we show this minimax risk is equivalent to the minimax risk $\rho_n^*$ of an estimation problem with $2$ unknown parameters. We leverage this reduction to establish a second-order risk expansion $\rho_n^* = n^{-1} - Cn^{-4/3} + o_n(n^{-4/3})$ for an explicit constant $C$ related to the Airy function. The minimax risk is attained by Bernoulli randomization with a nonlinear shrinkage estimator. Our results show that standard procedures such as complete randomization with difference in means are only minimax optimal up to first order in $n.$ We derive further results on admissibility of these procedures and discuss the practical implications of our results.
I study the optimal design and analysis of randomized experiments for estimating finite-population average treatment effects when potential outcomes are known to be bounded, as with binary outcomes. Among all assignment mechanisms and a broad class of affine estimators, worst-case mean-squared error (MSE) is minimized...
We study expected improvement (EI) for minimizing a deterministic function $f$ in the RKHS $\mathcal H_k$ of a continuous positive-semidefinite kernel $k$ on a nonempty compact set $\mathcal X\subset\mathbb R^d$. Function values are observed exactly, and EI is computed from a fixed zero-mean Gaussian-process model with...
Emmanuel Vazquez, S. Petit· arXiv.org· 0 citations
Given $[0,1]$-valued random variables $X_1,\dots,X_n$ such that $\mathbb{E}[X_i | X_1,\dots,X_{i-1}]= \mu$ for all $i$, we propose a new nonasymptotic confidence interval for $\mu$ that is obtained by inverting terminal e-values generated by a novel betting strategy. When the data are iid, its limiting width matches th...
Diego Martinez-Taboada, Aaditya Ramdas· 1 citation
We study how fast experimental designs can approach the semiparametric efficiency bound in finite samples, as measured by the excess variance of unadjusted treatment effect estimation. We prove an impossibility theorem: under weak conditions, no design can approach the variance bound uniformly over smooth outcome model...
In the classical normal means problem, independent train--test folds can be constructed by perturbing the data with normal randomization. Averaging over $K$ such folds yields a cross-validation estimator whose bias depends on the marginal distribution of the randomization variables, while its variance depends on their...
S. Chattopadhyay, Si-Fan Liu, Snigdha Panigrahi· 0 citations
We study finite-sample valid tests of the one-sided mean hypothesis $H_0:\mu\leq 1$ against $H_1:\mu>1$ for nonnegative random variables. To do so, we develop a leave-one-out dual certificate framework, where certain pointwise inequalities imply p-value validity under the conditional mean null $\mathbb{E}[X_i\mid\mathb...
Yi-Fan Zhu, John C. Duchi· 0 citations
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