Second Order Chebyshev-Edgeworth and Cornish-Fisher Expansions for Distributions of Statistics Constructed from Samples with Random SizesстатьяИсследовательская статья
Аннотация:In practice, we often encounter situations where a sample size
is not defined in advance and can be a random value. In the present paper second order
Chebyshev--Edgeworth and Cornish--Fisher expansions based of Student's t- and Laplace
distributions and their quantiles are derived for samples with random size of a special
kind, using general transfer theorem, which allows to construct asymptotic expansions for
distributions of randomly normalized statistics from the distributions of the considered nonrandomly
normalized statistics and of the random size of the underlying sample. Recently,
interest in Cornish--Fisher expansions has increased because of study in risk management.
Widespread risk measure Value at Risk (VaR) substantially depends on the quantiles of
the loss function, which is connected with description of investment portfolio of financial
instruments.