In statistics of extremes, the upper tail inference is usually based on the sample values over a high threshold. In a semiparametric framework, we consider the probability-weighted moment estimator of a positive Extreme value Index. Due to the specificity of the properties of the estimator, a direct estimation of an "optimal" threshold is not straightforward. In this talk, we consider two adaptive procedures for choosing such a threshold. The performance of the methods will be analysed with a simulation study. An illustration with a real dataset in the field of insurance is also provided.