Political scientist

Cyrus Samii is a political scientist at New York University whose methodological work concerns quantitative field research and causal inference. His academic biography connects the design of randomized controlled trials to empirical social research.^[ref]

With Peter M. Aronow, Samii studied sampling designs in which every unit can be observed but some pairs can never be observed together. The distinction matters: positive individual inclusion probabilities suffice for an unbiased estimator of a finite population total, whereas the usual Horvitz-Thompson variance estimator also needs pairwise inclusion positivity.^[ref]

An original two-unit example makes the single-draw variance identifiability obstruction explicit. Fix two unknown population values $y_1,y_2$ and choose one index $J$ with probabilities $1/2,1/2$. The Horvitz-Thompson estimator is $\hat{T}=2y_J$, soAn estimator based only on the selected index and its observed value has expected value of the form $[a(y_1)+b(y_2)]/2$. Such an additive expression cannot equal $(y_1-y_2{)}^2$ for every pair of real values. Taking the mixed finite difference at $(0,0),(1,0),(0,1),(1,1)$ gives zero for the additive expression butfor the desired variance. Thus a single draw permits an unbiased estimator of the total but no universally unbiased estimator of its sampling variance. Independent auxiliary randomization cannot repair this: averaging that randomness still gives functions $a$ and $b$ of the same observed data.

This is a restriction imposed by the observation mechanism, rather than a shortage of algebraic ingenuity. It motivates separating design-based inference about a total from the additional information needed to quantify its uncertainty.

Peter M. Aronow develops statistical methods for causal inference, particularly design-based inference. Yale's institutional biography identifies research on complex experimental designs, network settings and incomplete survey data alongside appointments spanning political science and statistics.^[ref]

His joint work with Cyrus Samii studies how to estimate sampling variance when a sampling design never observes some pairs together. A missing product cannot simply be deleted from the population variance formula: doing so can produce either sign of bias. Their construction uses Young inequality to bound unobserved products by individually estimable powers and obtain a conservative variance estimator.^[ref]

For an original exact illustration, choose one of two fixed values $y_1,y_2$ with equal probabilities. As in the single-draw variance identifiability obstruction, the Horvitz-Thompson estimator $2y_J$ has true variance $V_p=(y_1-y_2{)}^2$. Retaining only diagonal contributions gives $D=2y_J^2$, withOpposite signs therefore produce downward bias. The elementary inequality $-2ab\le a^2+b^2$, obtained from $(a+b{)}^2\ge 0$, instead givesConsequently $C=4y_J^2$ is a conservative variance estimator for this stipulated sampling design; its excess in expected value is exactly $(y_1+y_2{)}^2$.

With $(y_1,y_2)=(3,-1)$, the true variance is16. The two possible values of $D$ are18 and2, averaging10; those of $C$ are36 and4, averaging20. Although ${\mathbb{E}}_{p}C\ge 16$, a realized value of $C$ can be below16. Conservativeness here is an expectation inequality, rather than a bound for every sample. By itself it also does not prove a specified confidence interval coverage probability.