The New England Journal of Statistics in Data Science

In extreme value analysis, the impact of rounding in data, a form of quantization, on statistical inferences beyond point estimation has not been comprehensively studied. This paper addresses these challenges by considering rounded data as interval-censored. The maximum likelihood estimators of the model parameters tailored to account for interval censoring are asymptotically unbiased and efficient. Further, we adapt classic goodness-of-fit tests, such as the Anderson-Darling test, for rounded data based on the maximum likelihood estimator. The resulting tests have appropriate sizes and considerable power. One application of such tests is threshold selection for the peak over threshold approach in extreme value analysis. The efficacy of our estimation approach and the goodness-of-fit tests are demonstrated through a simulation study involving data rounded from generalized Pareto distributions. Applying this method to precipitation data from 18 stations in eastern Washington, an area with typically low precipitation and expecting a significant rounding effect, we observe narrower interval estimates of return levels.