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ISSN : 1226-0657

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Vol.1 No.1
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Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
1994, v.1 no.1, pp.19-24
Jee, Eun-Sook
Jee,, E. (1994). . Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 1(1), 19-24.
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Abstract

Let P be a probability measure on the real line with Lebesque-density f. The usual estimator of the distribution function (≡df) of P for the sample <TEX>$\chi$</TEX><TEX>$_1$</TEX>,…, <TEX>$\chi$</TEX><TEX>$\_$</TEX>n/ is the empirical df: F<TEX>$\_$</TEX>n/(t)=(equation omitted). But this estimator does not take into account the smoothness of F, that is, the existence of a density f. Therefore, one should expect that an estimator which is better adapted to this situation beats the empirical df with respect to a reasonable measure of performance.(omitted)

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Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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