统计研究
統計研究
통계연구
Statistical Research
2014年
2期
91~95
,共null页
Copula 随机模拟 参数和半参数估计方法 稳健性
Copula 隨機模擬 參數和半參數估計方法 穩健性
Copula 수궤모의 삼수화반삼수고계방법 은건성
Copula; Stochastic Simulation; Parametric and Semiparametric Estimation Methods; Robustness
本文主要是在极大似然法的基础上，研究Copula的参数和半参数方法的估计效果。通过随机模拟，比较各个估计量的偏差、均方误差和赤迟信息准则，得知两步极大似然参数估计方法受边际分布的影响较大。一旦边际分布拟合出现误差，该方法的稳健性会很差。一是估计出的Copula参数会有较大的偏差和均方误差，二是赤迟信息准则的结果显示，该方法会错误地指定Copula函数类。相比之下，半参数估计不受边际分布的影响，稳健性要好。因此在估计Copula参数，特别是无法确定边际分布函数类型时，应该用半参数方法而不是参数方法。
本文主要是在極大似然法的基礎上，研究Copula的參數和半參數方法的估計效果。通過隨機模擬，比較各箇估計量的偏差、均方誤差和赤遲信息準則，得知兩步極大似然參數估計方法受邊際分佈的影響較大。一旦邊際分佈擬閤齣現誤差，該方法的穩健性會很差。一是估計齣的Copula參數會有較大的偏差和均方誤差，二是赤遲信息準則的結果顯示，該方法會錯誤地指定Copula函數類。相比之下，半參數估計不受邊際分佈的影響，穩健性要好。因此在估計Copula參數，特彆是無法確定邊際分佈函數類型時，應該用半參數方法而不是參數方法。
본문주요시재겁대사연법적기출상，연구Copula적삼수화반삼수방법적고계효과。통과수궤모의，비교각개고계량적편차、균방오차화적지신식준칙，득지량보겁대사연삼수고계방법수변제분포적영향교대。일단변제분포의합출현오차，해방법적은건성회흔차。일시고계출적Copula삼수회유교대적편차화균방오차，이시적지신식준칙적결과현시，해방법회착오지지정Copula함수류。상비지하，반삼수고계불수변제분포적영향，은건성요호。인차재고계Copula삼수，특별시무법학정변제분포함수류형시，응해용반삼수방법이불시삼수방법。
In this paper, we study the efficiency of parametric and semiparametric methods of estimating Copula by maximum likelihood method. Comparing the bias, mean square error and Akaike information criterion of all estimators by stochastic simulation, we obtain that the marginal distributions have much impact on parametric method such as two step maximum likelihood method. Once the goodness fit of the marginal distributions is not good enough, the robustness of this method is quite bad. Specifically, it is observed that the bias and mean square error of parameter estimators for Copula function are large. In addition the Akaike information criterion implies that two-steps maximum likelihood method may indicate wrong type of Copula function. By contrast, semiparametric method is not affected by the marginal distributions and has a robust estimator. Therefore, for estimating the parameters of Copula, we should use the semiparamertrie rather than parametric method when the marginal distributions can not be certainly determined.
