Brown, Lawrence DLow, Mark G2023-05-232023-05-2319962016-08-08https://repository.upenn.edu/handle/20.500.14332/47619A general constrained minimum risk inequality is derived. Given two densities fθ and f0 we find a lower bound for the risk at the point θ given an upper bound for the risk at the point 0. The inequality sheds new light on superefficient estimators in the normal location problem and also on an adaptive estimation problem arising in nonparametric functional estimation.adaptive estimationsuperefficient estimatorsnonparametric functional estimationminimum risk inequalitieswhite noise modeldensity estimationnonparametric regressionStatistics and ProbabilityArticle