Moderate deviations and law of the iterated logarithm in L-1(R-d) for kernel density estimators

作者：Gao Fuqing^*

来源：Stochastic Processes and Their Applications, 2008, 118(3): 452-473.

DOI：10.1016/j.spa.2007.04.010

• kernel density estimator
• moderate deviations
• law of the iterated logarithm

Let f(n)(x) be the non-parametric kernel density estimator of a density function f (x) based on a kernel function K. In this paper, we first prove two moderate deviation theorems in L-1(R-d) for {f(n)(X), n >= 1}. Then, as an application of the moderate deviations, we obtain a law of the iterated logarithm for {parallel to f(n) - Ef(n) parallel to(1), n >= 1}.

• 出版日期2008-3
• 单位武汉大学