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Laplace regression

In the model

Y_{i} ∣ X_{i} \sim Laplace (X_{i}^{T} β, σ),

maximum likelihood minimizes the sum of absolute residuals

S (β) = \sum_{i} ∣ Y_{i} - X_{i}^{T} β ∣.

The scale estimate is

σ = S (β) / n

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 Ancestors (8)

 Synonyms (1)

Least absolute deviations