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Fisher tested the fit of Gaussian linear models using replicated observations. We refine this method by (1) constructing near-replicates using an optimal nonbipartite matching and (2) defining a distance that focuses on predictors important to the model’s predictions. Near-replicates may not exist unless the predictor set is low-dimensional; the test addresses dimensionality by betting that model failures involve a subset of predictors important in the old fit. Despite using the old fit to pair observations, the test has exactly its stated level under the null hypothesis. Simulations show the test has reasonable power even when many spurious predictors are present.
This is an Accepted Manuscript of an article accepted by Taylor & Francis for publication in Technometrics and posted online 19 July 2016, available online: http://www.tandfonline.com/10.1080/00401706.2016.1212737
combinatorial optimization, network optimization, Tukey's test for nonadditivity
Pimentel, S. D., Small, D. S., & Rosenbaum, P. R. (2017). An Exact Test of Fit for the Gaussian Linear Model using Optimal Nonbipartite Matching. Technometrics, 59 (3), 330-337. http://dx.doi.org/10.1080/00401706.2016.1212737
Date Posted: 25 October 2018
This document has been peer reviewed.