Estimating quantiles with Linex loss function. Applications to VaR estimation

• Autorzy: Ryszard Zieliński
• Języki publikacji: EN

Abstrakty

EN

Sometimes, e.g. in the context of estimating VaR (Value at Risk), underestimating a quantile is less desirable than overestimating it, which suggests measuring the error of estimation by an asymmetric loss function. As a loss function when estimating a parameter θ by an estimator T we take the well known Linex function exp{α(T-θ)} - α(T-θ) - 1. To estimate the quantile of order q ∈ (0,1) of a normal distribution N(μ,σ), we construct an optimal estimator in the class of all estimators of the form x̅ + kσ, -∞ < k < ∞, if σ is known, or of the form x̅ + λs, if both parameters μ and σ are unknown; here x̅ and s are the standard estimators of μ and σ, respectively. To estimate a quantile of an unknown distribution F from the family ℱ of all continuous and strictly increasing distribution functions we construct an optimal estimator in the class 𝓣 of all estimators which are equivariant with respect to monotone transformations of data.

Kategorie tematyczne

• 62G05: Estimation
• 62F10: Point estimation

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2005
• Tom: 32
• Numer: 4
• Strony: 367-373

Daty

wydano

2005

Twórcy

autor

Ryszard Zieliński

• Institute of Mathematics, Polish Academy of Sciences, P.O. Box 21, 00-956 Warszawa, Poland

Identyfikatory

DOI

10.4064/am32-4-1