Application Of Empirical Likelihood Estimation In Risk Measure

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.