| Nonparametric and parametric methods are commonly used in flood frequency analysis. Parametric method must assume that the types of population distribution, but if the assumption does not match with the observed series, it is hard to ensure the accuracy of its estimation. With the breakthrough and progress in its theory, nonparametric statistics do not assume its population distribution, so it is increasingly important in the application and research of flood frequency calculation. The paper investigated and applicated two nonparametric transference models—nonparametric density transference model and transference regression model based on the study, summary and reference of the nonparametric statistics theory which researched by Dr. Danyao and Dongjie. The content and conclusions of this paper are as follows:(1) Nonparametric estimation and transformation theory. This paper introduced the selection principle and method about a reasonable kernel function and bandwidth based on the nonparametric kernel density estimation and kernel regression estimation. The proper selection of kernel function and window width (especially the latter) greatly impact on the estimation accuracy. Taking into account the hydrological characteristics and the precision of calculation, this paper selected the exponential function as kernel function and used the classical Least-Squares Cross-Validation (LSCV) method for obtaining the best bandwidth. Nonparametric kernel estimation has less precise in small samples, but the observed flood data length in China are generally shorter, so, it is necessary to combine transformation theory and nonparametric kernel estimation. The estimated curve of transformed sample is relatively smooth, which also will minimize bias and variance.(2) Application of nonparametric density transference model. The paper described the main idea and method of establishing nonparametric density transference model, discussed the error and convergence from the theoretical, and gived the specific algorithm of the transformation and iteration. In this paper, statistical tests used to verify the robustness of the model, and the relative error and relative standard deviation were used as its evaluation criteria. The analysis of 96 kinds of statistical program showed that nonparametric density transference model is more robust than the parametric model, because it has nothing to do with its population distribution. Finally, nonparametric density transference model and two parameter models (P3/MOM and LP3/MOM) are used to flood frequency analysis and calculation of year maximum floods peak flow in 12 stations in Shanbei, and the comparative analysis shows that can be as a method to calculate the designed flood frequency. Comparing the frequency curves which are nonparametric density transference model and two parameter models fitting the observed data, we can find that nonparametric density transference model can reflect the flood peak shape of population density, and can better fit the larger sample points, all of these are the parameter model can not match.(3) Application of nonparametric transference regression model. Based on the introduction on the theory of transference regression model, the paper discussed the error and convergence of this model, thus we can effectively use the transformation iterative multiplication and addition iteration in the transformation to ensure accuracy and improve the convergence rate. To minimize the bias and variance at the same time, the paper established transference regression model with the sample empirical distribution function. For transference regression model, the paper also proved it is robust by statistical test, and applied the modle to the calculation of flood frequency analysis in Shanbei. The application result show that transference regression model also is an appropriate method to calculate the designed value of flood frequency, and the capacityof fitting the observered data much better than the parametric model.
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