Abstract
LetZt be a null recurrent diffusion on ℝp with generatorG=(1/r)∇·(r∇) for smooth positiver. This note constructs an independent recurrent diffusionZ′ton ℝ1 such that (Zt, Z′t)is transient in ℝp+1. This resolves negatively an old question in simultaneous estimation: Is there an admissible but not Bayes estimatorσ(X) of the mean of a multivariate normal distribution for quadratic loss with the property: for every admissible σ′(X′), whereX′ is normal and independent ofX, (δ, δ′) remains admissible in the combined problem obtained by summing the component losses?
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