【作者】 董洁；

【导师】 谢悦波； 李文家；

【作者基本信息】 河海大学 ， 水文学及水资源， 2005， 博士

【摘要】 本文把非参数统计理论和变换理论结合起来，分别构造了三种非参数统计变换模型，在此基础上探讨了这三种模型在洪水频率分析中的适用性，为洪水频率分析提供了另外一种参考方法。 首先回顾了非参数统计在水文水资源应用的现状。指出非参数统计与参数统计计算方法的不同特点，及其优缺点。提出了把变换理论与非参数统计理论结合起来作为本论文的研究思路。建立了适用于洪水频率分析的非参数密度变换模型、变换回归模型和考虑历史洪水的洪水频率分析模型。从理论上讨论了非参数变换模型的收敛性、相合性等，详细介绍了建模的思想和方法，从稳健性的角度用统计试验方法论证了以上模型的稳健性。影响非参数核估计精度的因素主要是核函数及窗宽的选择，特别是窗宽对核估计的结果影响很大。用变换核估计方法克服了无偏性和最小方差要求的矛盾，避开了窗宽选择的难题。用变换方法对样本进行变换得到新样本，新样本对应的函数曲线比较平缓，估计点的真实值相差很小，可以用较多的点平滑，不致产生太大的偏差。最佳函数也比较平缓，平滑偏差小，从而可以取较大窗宽使方差也减小。 最后，通过对宜昌站，小浪底站和沁河的五龙口水文等站的年最大洪峰流量采用适线法和非参数变换模型进行洪水频率分析计算，结果显示，方法是可行的，特别是针对适线法拟合不太理想的水文数据，非参数变换模型具有较好的稳健性。更多还原

【Abstract】 This thesis is aimed to integrate the theory of nonparametric statistics and that of transference, establish three nonparametric statistical transference models, explore their applicability in analyzing floods frequency, and provide an alternate method to floods frequency analysis. Firstly , the thesis reviews the condition of the application of nonparametric statistics in hydrology and water resources and points out the difference of nonparametric statistics and parameter statistics in calculation method as well as their advantages and disadvantages. Secondly, it suggests integrating the theory of transference and that of nonparametric statistics as its research focus. Thirdly, it establishes nonparametric density transference model, transference regression model, and floods frequency-analyzing model, which are all applicable to floods frequency analysis. Theoretically, it discusses the consistency and asymptotic behavior of nonparametric transference model, introduces the idea and methods of model building in detail and testifies the stability of the models by means of statistical experimentation. The main factor influencing nonparametric kernel estimation accuracy lies in the choice of kernel function and bandwidth especially bandwidth has an enormous influence on the result of kernel estimation. Adopting the method of transformed kernel estimate helps overcome the contradiction of non bias and minimum mean square error requirement and avoid the difficulty in choosing bandwidth. With the help of transference method, a new sample can be made available. For its corresponding function curve is smoother and the gap of the true value of the statistical points is smaller, using more smooth points can avoid making big errors/deviations. And what’s more, optimal function is more even and bias is small, as a result, mean square error diminishes by choosing bigger bandwidth Finally, based on curve-fitting method and non-parameter model, analyses and calculations are conducted on the floods frequency of yearly maximum floods peak flow in Yichang Station, Xiaolangdi Station and Qinhe-based Wulongkou Hydrometric Station, the results of which proves the feasibility of the method. In particular, non-parameter transference model has better stability in contrast to the less ideal hydrological data of curve-fitting method.更多还原