On equivalencies between design-based and regression-based variance estimators for randomized experiments

By Cyrus Samii, P. M. Aronow. 2012

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The Econometrics of Randomized Experiments (2016, background): “See for additional discussions Lesaffre and Senn (2003), Samii and Aronow (2012), Rosenbaum (2002), Lin (2013), Schochet (2010), Young (2016), Senn (1994).”
Generalizing from Survey Experiments Conducted on Mechanical Turk: A Replication Approach (2018, methodology): “In all cases, I employed the Neyman variance estimator, equivalent to a standard variant of heteroskedasticity robust standard errors (Samii and Aronow 2012).”
Estimating Average Causal Effects Under General Interference (2012, background): “Results for this estimator (including equivalencies to alternative, common estimators) are established in Samii and Aronow (2012) in the case of complete random assignment of a binary treatment variable.”
SHARP BOUNDS ON THE VARIANCE IN RANDOMIZED EXPERIMENTS (2014, background): “LEE The estimate V̂ a n is also produced by common estimators that presuppose sampling from an infinite superpopulation, including heteroskedasticityrobust variance estimators [12, 16] and the standard variance estimate for mean differences between independent groups [13].”
A Class of Unbiased Estimators of the Average Treatment Effect in Randomized Experiments (2013, methodology): “[13] and [14] cancel in expectation and, therefore, the terms do not lead to bias in the estimation of YT 1 or Y T 0 .”
Agnostic notes on regression adjustments to experimental data: Reexamining Freedman's critique (2012, background): “Tukey (1991) suggests adjustment “perhaps as a supplemen- 8For details, see Hinkley and Wang (1991), Angrist and Pischke [(2009), pp. 294–304], or Samii and Aronow (2012). tal analysis” for “protection against either the consequences of inadequate randomization or the (random) occurrence of an…”
A paradox from randomization-based causal inference (2014, methodology): “Schochet (2010), Samii and Aronow (2012), Lin (2013) and Imbens and Rubin (2015) pointed out that we can solve this problem by using the Huber– White heteroskedasticity-robust variance estimator (Huber, 1967; White, 1980), and the corresponding Wald test is asymptotically the same as Neyman’s test.”
Bridging Finite and Super Population Causal Inference (2017, background): “Also see Samii and Aronow (2012) and Lin (2013), who provide alternative discussions of super population regression-based variance estimators under the finite population framework.”
General Forms of Finite Population Central Limit Theorems with Applications to Causal Inference (2016, methodology): “and linear regression with full treatment-covariate interactions using the Huber–White variance estimator. We supplement his result with “optimality” and a rigorous proof of the asymptotic Normality. Samii and Aronow (2012) focused on comparison of regression-based and randomization-based standard e”