This paper considers a series estimator of 𝗕E [α (Y) λ (X) = λ̄], (α,λ) ∈ 𝒜 × Λ, indexed by function spaces, and establishes the estimator's uniform convergence rate over λ̄ ∈ R, α ∈ 𝐑, and λ ∈ Λ, ...

P. J. Bickel, P. W. Millar, UNIFORM CONVERGENCE OF PROBABILITY MEASURES ON CLASSES OF FUNCTIONS, Statistica Sinica, Vol. 2, No. 1 (January 1992), pp. 1-15 ...