Answers are grounded in this paper and cite their sources.
Minimum distance estimates are studied at the N(θ, 1) model. Estimates based on a non-Hilbertian distance μ (μ = Kolmogorov-Smirnov, Levy, Kuiper, variation and Prohorov) can exhibit very large variances, or even outright inconsistency, at distributions arbitrarily close to the model in terms of μ-distance. For Hilbertian distances (μ = Cramer-von Mises, Hellinger) this problem does not seem to occur. Geometric motivation for these results is provided.
No takes yet. Share an insight, caveat, or question.
Donoho et al. (1988) studied this question.
Synapse has enriched 5 related papers. Consider them for comparative context: