ACTA issues

A law of the iterated logarithm for kernel density estimator under random censorship and truncation

Sze Man Tse

Acta Sci. Math. (Szeged) 74:1-2(2008), 399-412

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.)