Stochastic Modeling, Data Analysis and Statistical Applications

TitleStochastic Modeling, Data Analysis and Statistical Applications
Publication TypeBook Chapter
Year of Publication2015
AuthorsGomes IM, Caeiro F, Figueiredo F
EditorFilus L, Oliveira T, Skiadas CH
ChapterA Partially Reduced-Bias Value-at-Risk Estimation Procedure

For any level q, 0 < q < 1, and on the basis of a sample X := (X1, ..., Xn) of either independent, identically distributed or possibly weakly dependent and stationary random variables from an unknown model F with a heavy right-tail function, the value-at-risk at the level q, the size of the loss that occurred with a small probability q, is estimated by a new partially reduced-bias semi-parametric procedure. With the notation (X1:n <= ... <= Xn:n) for the set of ascending order statistics associated with the available sample X, such a procedure is based on the mean-of order-p of the set of statistics U := \{Uik := Xn-i+1:n / Xn-k:n; 1 <= i <= k < n\}, with p a non-negative number and k + 1 the number of top order statistics used in the estimation.