**Syntax**

` >>> QUADRATIC-LINEAR: c`

**Parent Command**

` >> OPTION
`

**Subcommand**

` -
`

**Description**

This command selects a quadratic-linear objective function. Given this estimator, the objective function to be minimized is a combination of least-squares for small residuals and the first norm for residuals larger than *c*-times the prior standard deviation:

where

with

This objective function does not correspond to a standard probability density function. It has the general characteristic that the weight given individual residuals first increases quadratically with deviation, then only linearly to reduce the impact of outliers. For *c* –> infinity, the estimator is identical to least-squares; for *c* –> 0, it approaches the L_{1}-estimator. Note that this objective function is minimized using the standard Levenberg-Marquardt algorithm which is designed for a quadratic objective function. Since the function is quadratic for y < *c*, the Levenberg-Marquardt algorithm is usually quite efficient.

**Example**

` > COMPUTATION
>> OPTION
>>> use a QUADRATIC-LINEAR robust estimator with a constant `

*c*: 1.0 <<< <<

**See Also**

` >>> ANDREW | >>> CAUCHY | >>> L1-ESTIMATOR | >>> LEAST-SQUARES
`