Generalizations of the Kantorovich and Wielandt Inequalities with Applications to Statistics

Yunzhi Zhang, Xiaotian Guo, Jianzhong Liu and Xueping Chen ()
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Yunzhi Zhang: School of Mathematics and Physics, Jiangsu University of Technology, Changzhou 213001, China
Xiaotian Guo: School of Mathematics and Physics, Jiangsu University of Technology, Changzhou 213001, China
Jianzhong Liu: School of Mathematics and Physics, Jiangsu University of Technology, Changzhou 213001, China
Xueping Chen: School of Mathematics and Physics, Jiangsu University of Technology, Changzhou 213001, China

Mathematics, 2024, vol. 12, issue 18, 1-13

Abstract: By utilizing the properties of positive definite matrices, mathematical expectations, and positive linear functionals in matrix space, the Kantorovich inequality and Wielandt inequality for positive definite matrices and random variables are obtained. Some novel Kantorovich type inequalities pertaining to matrix ordinary products, Hadamard products, and mathematical expectations of random variables are provided. Furthermore, several interesting unified and generalized forms of the Wielandt inequality for positive definite matrices are also studied. These derived inequalities are then exploited to establish an inequality regarding various correlation coefficients and study some applications in the relative efficiency of parameter estimation of linear statistical models.

Keywords: positive-definite matrix; correlation coefficient; kantorovich inequality; covariance matrix; mathematical expectation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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