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Abstract. In this paper, we consider the kernel density estimator constructed from the product-limit estimator of an unknown continuous distribution when the data are subjected to random left truncation and right censorship. We obtained a law of the iterated logarithm for the exact pointwise convergence rate of the kernel density estimator.
AMS Subject Classification
(1991): 62G05, 62G07, 62G20, 60F15
Keyword(s):
Law of the iterated logarithm,
strong approximation,
counting process,
martingales,
stochastic integrals,
product-limit estimator
Received June 8, 2007, and in final form April 15, 2008. (Registered under 6022/2009.)
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