**Syntax**

` >>> L1-ESTIMATOR`

**Parent Command**

` >> OPTION
`

**Subcommand**

` -
`

**Description**

This command selects the L_{1}-estimator, i.e., the objective function to be minimized is the sum of the weighted absolute residuals.

Minimizing the mean absolute deviation leads to a maximum-likelihood estimate if the errors follow a double exponential distribution.

The L_{1}-estimator should be used, for example, to minimize a cost function for the optimization of a cleanup operation. Furthermore, it can be used whenever the objective function of interest is a linear function of the model output (e.g., in a sensitivity analysis using command `>>> OBJECTIVE` in block `>> OPTION`). Note that this objective function is usually minimized using the Levenberg-Marquardt algorithm which is designed for a quadratic objective function. Minimization is therefore rather inefficient, requiring more iterations and a high initial Levenberg parameter. The downhill simplex algorithm (see command `>>> SIMPLEX)` can be used as an alternative.

**Example**

` > COMPUTATION
>> OPTION
>>> use L1-ESTIMATOR, then draw contours of the
>>> OBJECTIVE function based on : 10 points in the parameter space
<<<
<<`

**See Also**

` >>> ANDREW | >>> CAUCHY | >>> LEAST-SQUARES | >>> QUADRATIC-LINEAR
`