Title: Semiparametric Minimax Rates.
Authors: Robins, James; Tchetgen Tchetgen, Eric; Li, Lingling; van der Vaart, Aad
Published In Electron J Stat, (2009)
Abstract: We consider the minimax rate of testing (or estimation) of non-linear functionals defined on semiparametric models. Existing methods appear not capable of determining a lower bound on the minimax rate of testing (or estimation) for certain functionals of interest. In particular, if the semiparametric model is indexed by several infinite-dimensional parameters. To cover these examples we extend the approach of , which is based on comparing a "true distribution" to a convex mixture of perturbed distributions to a comparison of two convex mixtures. The first mixture is obtained by perturbing a first parameter of the model, and the second by perturbing in addition a second parameter. We apply the new result to two examples of semiparametric functionals:the estimation of a mean response when response data are missing at random, and the estimation of an expected conditional covariance functional.
PubMed ID: 29629001
MeSH Terms: No MeSH terms associated with this publication