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In this paper we will discuss asymptotic properties of a kernel estimator of excess distribution function (EDF). The excess distribution function takes an important role in extreme value analysis, sur...vival analysis, and so on. The excess distribution function is a conditional distribution function H_u(x) = P(X - u ≦ x｜X > u) (x > 0). Thus it is a ratio of the functions which relate to the distribution function X. If we can assume a parametric model, we can get an estimator of EDF. Also, using the empirical distribution function, a nonparametric estimator of EDF is obtained. Since the empirical distribution is not smooth, we propose a kernel type estimator of EDF, which gives us a smooth estimate, and discuss its mean squared errors, theoretically.show more
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