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Generalizations of the Kantorovich and Wielandt Inequalities with Applications to Statistics

Author

Listed:
  • 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)

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.

Suggested Citation

  • Yunzhi Zhang & Xiaotian Guo & Jianzhong Liu & Xueping Chen, 2024. "Generalizations of the Kantorovich and Wielandt Inequalities with Applications to Statistics," Mathematics, MDPI, vol. 12(18), pages 1-13, September.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:18:p:2860-:d:1478236
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    References listed on IDEAS

    as
    1. Xueping Chen & Jianzhong Liu & Jiandong Chen, 2022. "A new result on recovery sparse signals using orthogonal matching pursuit," Statistical Theory and Related Fields, Taylor & Francis Journals, vol. 6(3), pages 220-226, August.
    2. Litong Wang & Hu Yang, 2012. "Matrix Euclidean norm Wielandt inequalities and their applications to statistics," Statistical Papers, Springer, vol. 53(3), pages 521-530, August.
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