Summary
We establish a law of the iterated logarithm for a triangular array of independent random variables, and apply it to obtain laws for a large class of nonparametric density estimators. We consider the case of Rosenblatt-Parzen kernel estimators, trigonometric series estimators and orthogonal polynomial estimators in detail, and point out that our technique has wider application.
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Hall, P. Laws of the iterated logarithm for nonparametric density estimators. Z. Wahrscheinlichkeitstheorie verw. Gebiete 56, 47–61 (1981). https://doi.org/10.1007/BF00531973
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DOI: https://doi.org/10.1007/BF00531973