On the existence of strongly consistent rules for estimation andclassification

摘要

Suppose we observex₁,x₂,…ε𝒳 drawn i.i.d. accordingto some unknown distribution P selected from a family of distributions𝒫. Let f:𝒫→Λ be a parameterisation ofP∈𝒫. In this paper, we study necessary and sufficientconditions for the existence of strongly consistent estimators of f(P).A number of previous results along these lines are special cases of ourmain result