【作者】 王强；

【导师】 吴贤毅；

【作者基本信息】 华东师范大学 ， 概率论与数理统计， 2007， 硕士

【摘要】 经验似然方法是由Owen(1988)提出来的一种非参数统计推断方法。利用经验似然方法，可以在不知道数据来自何种分布族的的情况下，对参数进行点估计和区间估计，并且具有良好的渐近势。经验似然方法在统计和经济学中应用广泛，可以用来对总体均值，线性模型，部分线性单指标模型，估计方程，有偏抽样及删失数据等模型进行估计。这种方法可以看成是bootstrap方法的非重复抽样以及没有参数假设的似然方法。风险度量是经济学中，特别是保险中要重点考虑的问题。风险度量在一定的条件下，可以通过扭曲函数的变换而表示成风险(随机变量)的函数的数学期望的形式。在一定的条件下，可以用L-估计来构造估计量和进行区间估计，这里包括对PHT-measure及WT-measure的估计。但是在PHT-measure中，当0＜r≤1／2时，用L-估计由于渐近性得不到保证，不可用L-估计来做区间估计。在本文中，我们将改良经验似然估计的基本定理，使新的关于经验似然的结论可以应用到风险度量中来，使其可以对风险度量做区间估计。在一定的条件下，用经验似然所做的估计更具有一般性，通过模拟的结果，我们也可以看出，经验似然估计要比L-估计更为精确，也具有良好的渐近性，而且它也克服了L-估计中的一些不足之处。更多还原

【Abstract】 Empirical likelihood is a nonparametric method of statistical inference which was first put forward by Owen(1988). It can be used to find efficient estimator, and to construct confidence region with good asymptotic power property, without assuming the data to come from a known family of distribution. The method of empirical likelihood has been applied to inference for some important models including population mean, linear model,quantile . estimation equation. biased sampling , censored data and so on . Empirical likelihood can be thought of as a bootstrap that does not resample and as a likelihood without parametric assumptions.Risk measure is a very important problem in economics, specially in actuarial. Several authors have discussed that a number of risk measure can be expressed as the expectation of the risk under a change of measure accomplished using a distortion function. Under mild conditions , L-estimate can used to construct estimator and confidence region of risk measure . including PHT-measure and WT-measure. But when the parameter r of PHT-measure is between 0 and 1/2, L-estimate can’t be used construct confidence of PHT-measure, we should find other method to conquer this shortcoming.In this paper , we will develop the theorem of empirical likelihood and apply the new conclusion to estimate risk measure. Under poor conditions , the empirical likelihood method can construct empirical likelihood estimator and confidence region of risk measure, which bases on empirical distribution. In the paper, the empirical likelihood method of risk measure will compare with L-estimate of risk measure in simulation result. Empirical likelihood method not only overcomes some disadvantages of L-estimate of risk measure, but also is more accuracy than L-estimate.更多还原