Laws of the iterated logarithm for nonparametric density estimators |
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Authors: | Peter Hall |
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Institution: | (1) Dept. of Statistics, Australian National University, Box 4, 2600 Canberra, ACT, Australia |
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Abstract: | 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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