Manual Page for Command >>> ANDREW


Syntax
>>> ANDREW: c

Parent Command
>> OPTION

Subcommand
-

Description
This command selects a robust estimator named Andrews. Given this estimator, the objective function to be minimized is the sum of the cosine functions g(y), where y is the weighted residual:

S=Sum(g(y )) i=1,...,m

where:

with:

yi=ri/sigmai

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 with deviation, then decreases to reduce the impact of outliers. The parameter c indicates the deviation at which residuals are considered to be outliers. If the measurement errors happen to be close to a normal distribution with standard deviation sigma, then the optimal value for the constant c is c=2.1. Note that this objective function can be minimized using the standard Levenberg-Marquardt algorithm which is designed for a quadratic objective function. Since (1-cosine) can be reasonably well approximated by a quadratic function for small yi, the Levenberg-Marquardt algorithm is usually quite efficient.

Example
> COMPUTATION
>> OPTION
>>> use the robust estimator ANDREW with a constant c : 1.5
<<<
<<

See Also
>>> CAUCHY | >>> L1-ESTIMATOR | >>> LEAST-SQUARES | >>> QUADRATIC-LINEAR


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Page updated: July 29, 1997