Statistical analysis of rainfall extremes is mostly based on the assumption of error-free data, despite common knowledge about the widespread incidence of precipitation measurement bias and variability. The objective of this study is primarily to investigate the impact of measurement bias and variability in statistical classification and quantile estimates of rainfall extremes. A theoretical framework is presented for the analysis of moment coefficients and probability distributions for rainfall extremes corrupted by measurement bias and variability. Furthermore, methods are outlined for practical statistical analysis of error-corrupted rainfall extremes, based on maximum likelihood. Frequency inference and testing for the presence of measurement variability are the main topics. Modelling of data series is undertaken in order to exemplify the statistical assessment and the real-life impact of measurement error. It is shown that: (a) unaccounted measurement error may potentially cause a considerable degree of misspecification about the conventional moment and L-moment coefficients of variation, and the conventional moments of skewness and kurtosis; (b) the presence of measurement variability alone can cause significant and nonlinear quantile bias which further strongly increases with the additional presence of measurement bias; and (c) maximum likelihood estimation provides a general and efficient tool for assessing measurement error in extreme rainfall frequency analysis.