Summary
In general the α-quantile of a random variable is not uniquely determined. It is the aim of this paper to suggest a limit process for chosing exactly one α-quantile. Moreover a natural choice of a conditional α-quantile is suggested.
Similar content being viewed by others
References
Ando, T., andL. Amemiya: Almost everywhere convergence of prediction sequences inL p (1<p<∞). Z. Wahrscheinlichkeitstheorie verw. Geb.4, 1965, 113–120.
Freedman, D.: Markov Chains. San Francisco 1971.
Hoch, H.: Diplomarbeit. Konstanz 1980.
Landers, D., andL. Rogge: Best approximants inL ϕ-spaces. Z. Wahrscheinlichkeitstheorie verw. Geb.51, 1980, 215–237.
—: Natural choice ofL 1-approximants. Journal of Approximation Theory33, 1981a, 268–280.
—: Consistent estimation of the natural median. Statistics and Decision1, 1983, 269–284.
—: The Natural Median. Annals of Probability9, 1981b, 1041–1042.
—: Isotonic approximation inL S. Journal of Approximation Theory31, 1981c, 199–223.
Shintani, T., andT. Ando: Best approximants inL 1-space. Z. Wahrscheinlichkeitstheorie verw. Geb.33, 1975, 33–39.
Tomkins, R.J.: On conditional medians. Ann. Prob.3, 1975, 375–379.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Landers, D., Rogge, L. Natural α-quantiles and conditional α-quantiles. Metrika 31, 99–113 (1984). https://doi.org/10.1007/BF01915191
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF01915191