Clustering for Regional Time Trend in the Nonstationary Extreme Distribution

Since the estimation of tail properties requires a stationarity of observations, it is necessary to develop a de-trending method not dependent on underlying distributions for nonstationary hydrological processes. Moreover, de-trending has been independently applied to hydrological processes, even though the processes are observed in geometrically adjacent sites. This paper presents a distribution-free de-trending method for nonstationary hydrological processes. Our method also provides clustered regional trends obtained by sparse regularization in a general distribution. It aggregates the parameter estimation and clustering within a unified framework. In the simulation study, our proposed method has superiority over other compared methods with respect to MSE and variance of coefficients. In real data analysis, the clustered trends of the annual maximum precipitation in the South Korean peninsula are reported, and the patterns of the estimated trends are visualized.