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Least absolute deviations
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<p>Least absolute deviations (LAD), also known as least absolute errors (LAE), least absolute residuals (LAR), or least absolute values (LAV), is a statistical <a href="/facts/Optimality_criterion/PNnlYnxs">optimality criterion</a> and a statistical <a href="/facts/Optimization_(mathematics)/oRn8Iv5I">optimization</a> technique based on <a href="/facts/Maxima_and_minima/ADlgnyzV">minimizing</a> the sum of absolute deviations (also <i>sum of absolute residuals</i> or <i>sum of absolute errors</i>) or the <a href="/facts/L1_norm/gbad0Rv1"><i>L</i>1 norm</a> of such values. It is analogous to the <a href="/facts/Least_squares/50jIwbxC">least squares</a> technique, except that it is based on <i><a href="/facts/Absolute_value/dwJBpEs5">absolute values</a></i> instead of <a href="/facts/Square_(algebra)/Jzpq0R0z">squared values</a>. It attempts to find a <a href="/facts/Function_(mathematics)/CdReEKCh">function</a> which closely approximates a set of data by minimizing <a href="/facts/Errors_and_residuals/Ef0LgAS4">residuals</a> between points generated by the function and corresponding data points. The LAD estimate also arises as the <a href="/facts/Maximum_likelihood/0Yq2dpQD">maximum likelihood</a> estimate if the errors have a <a href="/facts/Laplace_distribution/teMwaLry">Laplace distribution</a>. It was introduced in 1757 by <a href="/facts/Roger_Joseph_Boscovich/TpAtNdUX">Roger Joseph Boscovich</a>. </p>