Manual Page for Command >>> L1-ESTIMATOR


Syntax
>>> L1-ESTIMATOR

Parent Command
>> OPTION

Subcommand
-

Description
This command selects the L1-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 L1-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


Back to Command Index

Page updated: July 29, 1997