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.