Lower quantiles for complete lattices

Schollmeyer, Georg (31. August 2017): Lower quantiles for complete lattices. Department of Statistics: Technical Reports, No.207

Abstract

In this technical report a notion of (lower) quantiles for data or random variables with values in a complete lattice is developed. We list a number of desirable properties a reasonable notion of quantiles should have and analyze for different proposals of quantiles, which of these properties they fulfill. It turns out that one of the constructions has acceptable properties and can thus be used for analyzing lattice-valued data.

• Item Type: Paper
• Keywords: lower quantile, complete lattice, level function, representation invariance, data depth
• Faculties: Mathematics, Computer Science and Statistics > Statistics > Technical Reports; Mathematics, Computer Science and Statistics > Statistics > Chairs/Working Groups > Foundations of Statistics and their Applications
• Subjects: 500 Science > 510 Mathematics
• Language: German