Least absolute deviations (LAD), also known as Least Absolute Errors (LAE), Least Absolute Value (LAV), or Least Absolute Residual (LAR) or the L1 norm problem, is a statistical optimization technique similar to the popular least squares technique that attempts to find a function which closely approximates a set of data. In the simple case of a set of (x,y) data, the approximation function is a simple ‘trend line’ in two-dimensional Cartesian coordinates. The method minimizes the sum of absolute errors (SAE) (the sum of the absolute values of the vertical ‘residuals’ between points generated by the function and corresponding points in the data). The least absolute deviations estimate also arises as the maximum likelihood estimate if the errors have a Laplace distribution. … Least Absolute Deviations (LAD)

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