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| Abstract |
For a kernel estimator of a density function, we obtain an asymptotic representation of a ackknife variance estimator of the kernel density estimator and prove its consistency. Assuming a bandwidth h_...n=cn^<-(1)/(4)> (c > 0), we also discuss an Edgeworth expansion with residual term o(n^<-1/2>) and its validity. Many papers have studied theoretical properties of a kernel density estimator. Especially mean integrated squared errors are precisely studied. The asymptotic distribution of the estimator is also discussed, and it is easy to show asymptotic normality. In this paper, we will discuss higher order approximation of the distribution of the kernel estimator. We will obtain an Edgeworth expansion, which takes an explicit form with residual term o(n^<-1/2>)show more
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1-Nishimoto