Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
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.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
367-373
Opis fizyczny
Daty
wydano
2005
Twórcy
autor
- Institute of Mathematics, Polish Academy of Sciences, P.O. Box 21, 00-956 Warszawa, Poland
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
DOI
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-am32-4-1