Refined solution to upper-bound problem for the expectations of order statistics from decreasing density on the average distributions. Issue 16 (18th August 2018)

• Record Type: Journal Article
• Authors: Goroncy, Agnieszka; Rychlik, Tomasz
• Is Part Of: Communications in statistics. Volume 47:Issue 16(2018)
• Page Start: 4029
• Page End: 4041
• Publication Date: 2018-08-18
• Subjects: Bernstein polynomial -- Decreasing density on the average -- Order statistic -- Sharp bound -- Variation diminishing property; 60E15 -- 62G32; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2017.1367813
• Languages: English
• ISSNs: 0361-0926

Abstract

ABSTRACT: Rychlik [ Metrika 77, 539–557, 2014] described sharp upper negative bounds for the expectations of low-rank order statistics, centered about the population mean and measured in the mean absolute deviation from the mean units, for the i.i.d. sequences with common distribution possessing decreasing density function on the average. The bounds coincide with the negatives of maximal values of complicated functions on the unit interval. Here, we provide more precise solutions to the maximization problems.