Testing composite hypotheses, Hermite polynomials and optimal estimation of a nonsmooth functional
Testing composite hypotheses, Hermite polynomials and optimal estimation of a nonsmooth functional
A general lower bound is developed for the minimax risk when estimating an arbitrary functional. The bound is based on testing two composite hypotheses and is shown to be effective in estimating the nonsmooth functional (1/n)∑|θi| from an observation Y∼N(θ, In). This problem exhibits some features that are significantly different …