Abstract
Maximum likelihood estimates are sufficient statistics in exponential families, but not in general. The theory of statistical curvature was introduced to measure the effects of MLE insufficiency in one-parameter families. Here, we analyze curvature in the more realistic venue of multiparameter families—more exactly, curved exponential families, a broad class of smoothly defined nonexponential family models. We show that within the set of observations giving the same value for the MLE, there is a “region of stability” outside of which the MLE is no longer even a local maximum. Accuracy of the MLE is affected by the location of the observation vector within the region of stability. Our motivating example involves “$g$-modeling,” an empirical Bayes estimation procedure.
Citation
Bradley Efron. "Curvature and inference for maximum likelihood estimates." Ann. Statist. 46 (4) 1664 - 1692, August 2018. https://doi.org/10.1214/17-AOS1598
Information