The penalty for assuming that a monotone regression is linear (Q1819508)
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scientific article; zbMATH DE number 3992699
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The penalty for assuming that a monotone regression is linear |
scientific article; zbMATH DE number 3992699 |
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The penalty for assuming that a monotone regression is linear (English)
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1987
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For jointly distributed random variables (X,Y) having marginal distributions F and G with finite second moments and F continuous, the proportion of Var(Y) explained by linear regression is \([Corr(X,Y)]^ 2\) while the proportion explained by E(Y\(| X)\) can be arbitrarily near 1. However, if the true regression, E(Y\(| X)\), is monotone, then the proportion of Var(Y) it explains is at most \(Corr[Y,G^{-1}(F(X))]\).
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penalty
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monotone regression
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expected squared-error loss
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intrinsic variation
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extralinear variation
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fixed margins
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linear regression
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