Isaac Scientific Publishing

Journal of Advanced Statistics

The Concept of Majorization in Experimental Designs

Download PDF (363 KB) PP. 117 - 124 Pub. Date: September 1, 2017

DOI: 10.22606/jas.2017.23002

Author(s)

  • Miltiadis S. Chalikias*
    Department of Business Administration, Piraeus University of Applied Science, Greece

Abstract

The information of interest is contained in the variance matrix, V = σ 2Q−1 , or equivalently in the information matrix Q . The problem of finding estimators minimizing a decreasing convex functional of the variance matrix or maximizing an increasing concave functional of the information matrix is crucial in statistics. There are several optimality criteria in bibliography. We explain how the concept of Majorization can be used to investigate optimal experimental designs.

Keywords

Majorization, direct effects, carry-over effects, universally optimality, F-Optimality, repeated measurements designs, saturated designs, row-column, factorial designs

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