Let X be a d-dimensional random vector with unknown density function f（z）=f（z1, ···, zd）, and let fn be teh nearest neighbor estimator of f proposed by Loftsgaarden and Quesenberry （1965）. In this paper, we established the law of the iterated logarithm of fn for general case of d≥1, which gives the exact pointwise strong convergence rate of fn.
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