Abstract
For regular parametric models, estimators converge uniformly at a rate n −1/2, and the limit distribution is normal with mean 0. The situation is different if the best possible rate is n −α, with α∈ (0, 1/2), as common for nonparametric models. In this case, uniformly attainable normal limit distributions with mean 0 are impossible.
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Pfanzagl, J. On Rates and Limit Distributions. Annals of the Institute of Statistical Mathematics 51, 755–778 (1999). https://doi.org/10.1023/A:1004043532578
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DOI: https://doi.org/10.1023/A:1004043532578