Bounds on dispersion of order statistics based on dependent symmetrically distributed random variables |
| |
Authors: | Krzysztof Jasiński Tomasz Rychlik |
| |
Institution: | 1. Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12, 87100 Toruń, Poland;2. Institute of Mathematics, Polish Academy of Sciences, Chopina 12, 87100 Toruń, Poland |
| |
Abstract: | We consider a fixed number of arbitrarily dependent random variables with a common symmetric marginal distribution. For each order statistic based on the variables, we determine a common optimal bound, dependent in a simple way on the sample size and number of order statistics, for various measures of dispersion of the order statistics, expressed in terms of the same dispersion measure of the single original variable. The dispersion measures are connected with the notion of M-functional of a random variable location with respect to a symmetric and convex loss function. The measure is defined as the expected loss paid for the discrepancy between the M-functional and the variable. The most popular examples are the median absolute deviation and variance. |
| |
Keywords: | Dependent identically distributed random variables Symmetric distribution Order statistic M-functional of location Dispersion Optimal bound |
本文献已被 ScienceDirect 等数据库收录! |
|