Stein's Paradox in Statistics¶
Efron, & Morris. (1977). Stein's Paradox in Statistics.
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Domain-specific¶
- Stein's Paradox
- In \(p\)-dimensional space, the maximum-likelihood estimator \(\bar{x}\) is, in expectation, farther from the true parameter vector \(\theta\) than \(\|\bar{x} - \theta\|\) suggests, because the expected squared distance \(E[\|\bar{x} - \theta\|^2] = p\sigma^2\) grows with dimension
This sourceThe geometric account of why the sample-mean vector sits too far from the true mean in high dimension, the expected squared distance growing in proportion to the number of coordinates.
- In \(p\)-dimensional space, the maximum-likelihood estimator \(\bar{x}\) is, in expectation, farther from the true parameter vector \(\theta\) than \(\|\bar{x} - \theta\|\) suggests, because the expected squared distance \(E[\|\bar{x} - \theta\|^2] = p\sigma^2\) grows with dimension
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