User`s guide

Smoothing Data

2-17

Robust Smoothing Procedure

If your data contains outliers, the smoothed values can become distorted, and

not reflect the behavior of the bulk of the neighboring data points. To overcome

this problem, you can smooth the data using a robust procedure that is not

influenced by a small fraction of outliers. For a description of outliers, refer to

“Marking Outliers” on page 2-27.

The Curve Fitting Toolbox provides a robust version for both the lowess and

loess smoothing methods. These robust methods include an additional

calculation of robust weights, which is resistant to outliers. The robust

smoothing procedure follows these steps:

1 Calculate the residuals from the smoothing procedure described in the

previous section.

2 Compute the robust weights for each data point in the span. The weights are

given by the bisquare function shown below.

is the residual of the ith data point produced by the regression smoothing

procedure, and MAD is the median absolute deviation of the residuals:

The median absolute deviation is a measure of how spread out the residuals

are. If r

is small compared to 6MAD, then the robust weight is close to 1. If

is greater than 6MAD, the robust weight is 0 and the associated data point

is excluded from the smooth calculation.

3 Smooth the data again using the robust weights. The final smoothed value

is calculated using both the local regression weight and the robust weight.

4 Repeat the previous two steps for a total of five iterations.

1( r

6MAD⁄()

)

–







6MAD<

6MAD≥

MAD median r()=