论文信息 - ON LEAST SQUARES ESTIMATES OF AN EXPONENTIAL TAIL COEFFICIENT

ON LEAST SQUARES ESTIMATES OF AN EXPONENTIAL TAIL COEFFICIENT

Consider a sample Zi,...,Z„ of i.i.d r.v.'s with tail behavior P{Zi > z) = r(z)exp(—Äz), where r( ) is an (unknown) regularly varying function as z —• oo, and R is a constant. Least squares estimators are proposed here for the problem of estimating the exponential tail coefiicient R. We mainly prove consistency of the proposed estimators. Some Simulation results are presented as well in order to illustrate the finite sample behavior. Herein, adaptive methods are suggested to determine the number k = k„ of upper order statistics, which should be taken into account for estimation. Without loss of generality we shall assume positivity of the random variables Zi

Josef Steinebach | J. Steinebach | J. Schultze | J. Schultze

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