An admissibility proof using an adaptive sequence of smoother proper priors approaching the target improper prior

A sufficient condition for the admissibility of generalized Bayes estimators of the location vector of spherically symmetric distribution under squared error loss is derived. This is as strong a condition as that of Brown [L.D. Brown, Admissible estimators, recurrent diffusions, and insoluble boundary value problems, Ann. Math. Statist. 42 (1971) 855-903] under normality. In particular we establish the admissibility of generalized Bayes estimators with respect to the harmonic prior and priors with slightly heavier tails than the harmonic prior. The key to our proof is an adaptive sequence of smooth proper priors approaching an improper prior fast enough to establish admissibility.