Using artificial censoring to improve extreme tail quantile estimates

Under certain regularity conditions, maximum‐likelihood‐based inference enjoys several optimality properties, including high asymptotic efficiency. However, if the distribution of the data deviates slightly from the model proposed, the statistical properties of inference methods based on maximum likelihood can quickly deteriorate. We focus on the situation when the interest lies in one of the tails of the distribution, e.g. when we are estimating a high or low quantile. In this case, it may be natural, if slightly unorthodox, to consider models that fit well the corresponding tail of the sample, rather than its whole range. For example, if we are interested in estimating the fifth percentile, we can pretend that all observations above the 10th percentile have been censored and fit a parametric censored model to the lower tail of the sample. Such an approach, which we call ‘artificial censoring’, has been studied in the engineering literature. We study a data‐dependent method to select the amount of artificial censoring and show that it compares favourably with the optimally chosen (‘oracle’) method, which is generally unavailable in practice. We also show that the artificial censoring approach can be applied to estimate tail dependence parameters in copula models, and that it performs well both in simulation and in real data studies.