Endpoint estimation for observations with normal measurement errors

This paper investigates the estimation of the finite endpoint of a distribution function when the observations are contaminated by normally distributed measurement errors. Under the framework of Extreme Value Theory, we propose a class of estimators for the standard deviation of the measurement errors as well as for the endpoint. Asymptotic theories for the proposed estimators are established while their finite sample performance is demonstrated by simulations. In addition, we apply the proposed methods to the outdoor long jump data to estimate the ultimate limit for human beings in the long jump.