Antieigenvalue techniques in statistics |
| |
Authors: | Morteza Seddighin |
| |
Institution: | Mathematics Department, Indiana University East Richmond, IN 47374, United States |
| |
Abstract: | In a number of his recent papers Karl Gustafson has outlined the similarities between the Antieigenvalue Theory he founded and several finite dimensional matrix optimization theorems for positive matrices arising in statistics. In this paper, we will show how the techniques that the author and Karl Gustafson have used for computation of Antieigenvalues can also be applied to prove and generalize these matrix optimization theorems in statistics. We will primarily focus on two techniques which we have used in Antieigenvalue computations in recent years. These two techniques are a two nonzero component property for certain class of functionals, and converting the matrix optimization problems in statistics to a convex programing problem. Indeed, these two techniques allow us to generalize some of the matrix optimization problems arising in statistics to strongly accretive operators on finite or infinite dimensional Hilbert spaces. |
| |
Keywords: | Antieigenvalue Antieigenvector Statistical efficiency Strongly accretive operator |
本文献已被 ScienceDirect 等数据库收录! |
|