Abstract
It seems that the curve of the Gaussian kernel density estimate is of ten flat as compared with that of true p.d.f., although its window width has been chosen suitably. This flatness sometimes causes a bad kernel estimate of density. In this paper we shall introduce a scale parameter into true p.d.f. to show the flatness of the curve of Gaussian kernel den sity estimate. We study the asymptotic properties of the scale parameter to propose a modified kernel density estimator. Some simulations show a superiority of the estimator.
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