Estimation, principal components and Hamiltonian systems (Q1086216)
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scientific article; zbMATH DE number 3983047
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Estimation, principal components and Hamiltonian systems |
scientific article; zbMATH DE number 3983047 |
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Estimation, principal components and Hamiltonian systems (English)
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1985
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The paper advocates the use of symplectic geometry to analyzing the structure of critical points of the least squares estimation function. The problem dealt with is that of fitting a plane, in particular a line, given a data set in \({\mathbb{C}}^ n\). The basic observation is that for the fitting of a line, the least squares estimation function can be regarded as a Hamiltonian defined on the orbit of the adjoint action of the unitary group.
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complete integrability
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symplectic geometry
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critical points
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least squares estimation
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Hamiltonian
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adjoint action
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0.87522644
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0.8583799
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0.8489207
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0.84662926
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0.8459727
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0.8440659
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0.84292895
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