Qualitative and Asymptotic Performance of SNP Density Estimators

The SNP estimator is the most convenient nonparametric method for simultaneously estimating the parameters of a nonlinear model and the density of a latent process by maximum likelihood. To determine if this convenience comes at a price, we assess the qualitative behavior of SNP in finite samples using the Marron--Wand test suite and verify theoretical convergence rates by Monte Carlo simulation. Our results suggest that there is no price for convenience because the SNP estimator is both qualitatively and asymptotically similar to the kernel estimator which is optimal.