Abstract

In extreme value analysis, quantization due to rounding causes biases in parameter estimation and incorrect sizes in goodness-of-fit testing. We treat rounded data as interval censored and estimate the parameters by maximizing the likelihood that accounts for interval censoring. The resulting estimator are asymptotically unbiased. Further, classic goodness-of-fit tests such as Anderson--Darling are adapted to discrete data resulted from rounding, which gives tests with correct sizes and substantial powers. Such tests have important implications in threshold selection for extreme value analyses. The performances of the estimation and goodness-of-fit are validated in a simulation study with rounded data from generalized Pareto distributions. In applications to the precipitation data of 18 eastern Washington stations, the proposed methods selected thresholds for more stations with more exceedances and, hence, more accurate return level estimations.