Functional partial canonical correlation

Huang, Qing Guang; Renaut, Rosemary A.

doi:10.3150/14-bej597

Cited by 2 publications

(1 citation statement)

References 20 publications

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“…Therefore, there will probably be no discrimination against gender in income. This designation of correlation has been used, for example, in scholarly articles [19][20][21][22][23].…”

Section: Methodsmentioning

confidence: 99%

Stability of Dependencies of Contingent Subgroups with Merged Groups: Vaccination Case Study

Macak

2021

Mathematics

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The answers to extreme phenomena both in nature and in business sectors are the constructions of the distribution of random variables with extreme values. Another area in which appropriate theoretical research is conducted regarding the influence of suppressor (third) variables in categorical data. When examining dependencies in PivotTables, we often find it necessary to merge data into larger sets (e.g., due to a greater number of theoretical frequencies lower than their critical value). A phenomenon many exist wherein the partial relation is stronger than the zero relation. For example, in such a combination, instability may occur, which indicates contingent subgroups with the merged group. The dependence of dependencies is practically manifested because the data of contingent subgroups indicate inconsistent (inverted) conclusions compared to the associated group. For this reason, this paper aimed to find the critical ratios of partial probabilities in the contingency table of subgroups of the original variables, and to determine the conditions of result consistency and contingency stability, including the proof. For practical use and for the ease of repeating the proposed procedure, the solution is based on a case study that compares the effectiveness of vaccination.

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“…Therefore, there will probably be no discrimination against gender in income. This designation of correlation has been used, for example, in scholarly articles [19][20][21][22][23].…”

Section: Methodsmentioning

confidence: 99%

Stability of Dependencies of Contingent Subgroups with Merged Groups: Vaccination Case Study

Macak

2021

Mathematics

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Efficient estimation of regularization parameters via downsampling and the singular value expansion

et al. 2016

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Abstract. The solution, x, of the linear system of equations Ax ≈ b arising from the discretization of an ill-posed integral equation with a square integrable kernel H(s, t) is considered. The Tikhonov regularized solution x(λ) is found as the minimizer of}. x(λ) depends on regularization parameter λ that trades off the data fidelity, and on the smoothing norm determined by L. Here we consider the case where L is diagonal and invertible, and employ the Galerkin method to provide the relationship between the singular value expansion and the singular value decomposition for square integrable kernels. The resulting approximation of the integral equation permits examination of the properties of the regularized solution x(λ) independent of the sample size of the data. We prove that estimation of the regularization parameter can be obtained by consistently down sampling the data and the system matrix, leading to solutions of coarse to fine grained resolution. Hence, the estimate of λ for a large problem may be found by downsampling to a smaller problem, or to a set of smaller problems, effectively moving the costly estimate of the regularization parameter to the coarse representation of the problem. Moreover, the full singular value decomposition for the fine scale system is replaced by a number of dominant terms which is determined from the coarse resolution system, again reducing the computational cost. Numerical results illustrate the theory and demonstrate the practicality of the approach for regularization parameter estimation using generalized cross validation, unbiased predictive risk estimation and the discrepancy principle applied for both the system of equations, and the augmented system of equations.

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Functional partial canonical correlation

Cited by 2 publications

References 20 publications

Stability of Dependencies of Contingent Subgroups with Merged Groups: Vaccination Case Study

Stability of Dependencies of Contingent Subgroups with Merged Groups: Vaccination Case Study

Efficient estimation of regularization parameters via downsampling and the singular value expansion

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