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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 dis...cussed, 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. Assuming a bandwidth h_n=O(n^<(-1)/4>), we also prove the validity of the expansion with residual term o(n^<(-3)/4>).show more
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