分野別セミナー

For the class of distortion risk measures, a natural estimator
has the form of L-statistics. We investigate the large sample
properties of general L-statistics based on weakly dependent data and
apply them to our estimator. Under certain regularity conditions, which
are somewhat weaker than the ones found in the literature, we prove that
the estimator is strongly consistent and asymptotically normal.
Furthermore we give a consistent estimator for its asymptotic variance
using spectral density estimators of a related stationary sequence. The
behavior of the estimator is examined using simulation in a simple
inverse-gamma autoregressive stochastic volatility model. It is found
both theoretically and by simulation study that the estimator always
suffers a negative bias. We will discuss bias correction methods in the
i.i.d. case and the possibility of their extension to the dependent case
using the bootstrap. Also, we indicate how the asymtotics for our
estimator can be extended to the estimator for law invariant risk
measures, which is obtained by dropping comonotonic additivity requirement.



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