Generalizations of the Kantorovich and Wielandt Inequalities with Applications to Statistics

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 pertain...

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Bibliographic Details
Published in:Mathematics (Basel) 2024-09, Vol.12 (18), p.2860
Main Authors: Zhang, Yunzhi, Guo, Xiaotian, Liu, Jianzhong, Chen, Xueping
Format: Article
Language:English
Subjects:
correlation coefficient
Correlation coefficients
covariance matrix
Inequalities
Inequalities (Mathematics)
Inequality
kantorovich inequality
Mathematical analysis
mathematical expectation
Matrices (mathematics)
Numerical analysis
Parameter estimation
positive-definite matrix
Random variables
Statistical analysis
Statistical models
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math12182860