Recent advances in nonparametric function estimation: Hydrologic applications

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Abstract
Nonparametric function estimation refers to methods that strive to approximate a target function locally, i.e., using data from a “small” neighborhood of the point of estimate. “Weak” assumptions, such as continuity of the target function and its differentiability to some order in the neighborhood, rather than an a priori assumption of the global form (e.g., linear or quadratic) of the entire target function are used. Traditionally, parametric assumptions (e.g., hydraulic conductivity is log normally distributed, floods follow a log Pearson III (LP3) distribution, annual stream flow is either log normal or gamma distributed, daily rainfall amounts are exponentially distributed, and the variograms of spatial hydrologic data follow a power law) have dominated statistical hydrologic estimation. Applications of nonparametric methods to some classical problems (frequency analysis, classification, spatial surface fitting, trend analysis, time series forecasting and simulation) of stochastic hydrology are reviewed.