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This paper provides a design-based framework for variance (bound) estimationin experimental analysis. Results are applicable to virtually any combinationof experimental design, linear estimator (e.g., difference-in-means, OLS, WLS)and variance bound, allowing for unified treatment and a basis for systematicstudy and comparison of designs using matrix spectral analysis. A proposedvariance estimator reproduces Eicker-Huber-White (aka. "robust","heteroskedastic consistent", "sandwich", "White", "Huber-White", "HC", etc.)standard errors and "cluster-robust" standard errors as special cases. Whilepast work has shown algebraic equivalences between design-based and theso-called "robust" standard errors under some designs, this paper motivatesthem for a wide array of design-estimator-bound triplets. In so doing, itprovides a clearer and more general motivation for variance estimators.

Unifying Design-based Inference: On Bounding and Estimating the Variance of any Linear Estimator in any Experimental Design