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Balancing and elimination of nuisance variables.
Noorbaloochi S, Nelson D, Asgharian M. Balancing and elimination of nuisance variables. The international journal of biostatistics. 2010 Jan 1; 6(2):Article 6.
Addressing covariate imbalance in causal analysis will be reformulated as an elimination of the nuisance variables problem. We show, within a counterfactual balanced setting, how averaging, conditioning, and marginalization techniques can be used to reduce bias due to a possibly large number of imbalanced baseline confounders. The notions of X-sufficient and X-ancillary quantities are discussed and, as an example, we show how sliced inverse regression and related methods from regression theory that estimate a basis for a central sufficient subspace provide alternative summaries to propensity based analysis. Examples for exponential families and elliptically symmetric families of distributions are provided.