On a consistent rank estimate in a linear structural model (Q2913233)
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scientific article; zbMATH DE number 6086808
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a consistent rank estimate in a linear structural model |
scientific article; zbMATH DE number 6086808 |
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On a consistent rank estimate in a linear structural model (English)
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26 September 2012
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rank estimate
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structural linear model
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Kendall's tau
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total least squares
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Theil-Sen estimate
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The author modifies the Theil-Sen estimator to the simple linear regression model with possible measurement errors in the regressor, and proves the consistency of the estimator for elliptical distributions of errors where Greiner's relation is valid. The key condition is a monotone relation between Kendall's population tau and the correlation. Parallelly, in the multiple linear regression model with measurement errors, she shows the coincidence of the Pearson and the total least squares estimators. The orthogonalization is an important tool for obtaining the results. A small simulation illustrates that the calculation of rank estimates is not any more problematic.
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