C.3 Extension to precision dependence The baseline model in Section 4.1 treats the sampling varianceσ2 i as observed and assumes precision independence, in the sense thatθ i ⊥ ⊥σi

showed that the generalized maximum likelihood estimator (GMLE) for the marginal densityf Y (y) converges at parametric rate (up to a logarithm factor) in Hellinger distance given that the mixing distribution has compact support or has a he · 2026