Spectral risk measures (SRMs) belong to the family of coherent risk measures. A natural estimator for the class of SRMs has the form of L-statistics. Various authors have studied and derived the asymptotic properties of the empirical estimator of SRM. We propose a kernel based estimator of SRM. We investigate the large sample properties of general L-statistics based on i.i.d and dependent observations and apply them to our estimator. We prove that it is strongly consistent and asymptotically normal. We compare the finite sample performance of our proposed kernel estimator with that of several existing estimators for different SRMs using Monte Carlo simulation. We observe that our proposed kernel estimator outperforms all the estimators. Based on our simulation study we have estimated the exponential SRM of four future indices-that is Nikkei 225, Dax, FTSE 100, and Hang Seng. We also perform a backtesting exercise of SRM.

翻译：光谱风险测量(SRMS)属于具有一致性风险测量措施的家庭。 SRM的自然测算器具有L-统计形式。各种作者研究并推断了SRM经验测算员的无症状性能。我们建议了SRM的内核测算仪。我们根据i.d和依赖性观测对一般L-统计的大规模样本特性进行了调查,并将其应用到我们的测算器上。我们证明,该类测算器具有很强的一致性和无症状的正常性。我们比较了我们提议的内核估测仪的有限样本性能与使用蒙特卡洛模拟对不同SRMMS现有测算员的样本性能。我们观察到,我们提议的内核测算器比所有测算器都高。根据我们的模拟研究,我们估计了四种未来指数的指数的指数(Nikkei 225, Dax, FTSE 100和Hang Sang)的指数的指数性能。我们还对SRM进行了反向测试。我们还对SRM进行了测试。