On Some alternative estimates of the adjustment coefficient in risk theory

Abstract Recently, Csorgo and Steinebach proposed to estimate the adjustment coefficient in risk theory via a quantile type estimate based upon a sequence of intermediate order statistics. In the present paper, further alternative estimators are discussed which may be viewed as convex combinations of a Hill type and a quantile type estimate. Consistency is proved and rates of convergence are studied. Some simulation results are presented to illustrate the finite sample behavior of the proposed estimators.

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