NPMLE attains parametric rates for density and posterior mean estimation in bounded-support Gaussian/Poisson mixtures when mixing is finitely discrete, and the LRT is asymptotically tight iff the mixing distribution is finitely discrete.
Then there exists a sequence of polynomials{q k}k∈N onΘsuch thatq 0(θ)≡1and, for anyk, k ′ ∈N, Z Θ qk(θ)q k′(θ) dg0(θ) =1 {k=k′}
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Adaptivity of the NPMLE to finitely discrete mixing distributions in Gaussian/Poisson mixtures
NPMLE attains parametric rates for density and posterior mean estimation in bounded-support Gaussian/Poisson mixtures when mixing is finitely discrete, and the LRT is asymptotically tight iff the mixing distribution is finitely discrete.