# Least absolute deviations

## Statistical optimality criterion / From Wikipedia, the free encyclopedia

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**Least absolute deviations** (**LAD**), also known as **least absolute errors** (**LAE**), **least absolute residuals** (**LAR**), or **least absolute values** (**LAV**), is a statistical optimality criterion and a statistical optimization technique based on minimizing the **sum of absolute deviations** (also *sum of absolute residuals* or *sum of absolute errors*) or the *L*_{1} norm of such values. It is analogous to the least squares technique, except that it is based on *absolute values* instead of squared values. It attempts to find a function which closely approximates a set of data by minimizing residuals between points generated by the function and corresponding data points. The LAD estimate also arises as the maximum likelihood estimate if the errors have a Laplace distribution. It was introduced in 1757 by Roger Joseph Boscovich.^{[1]}