User`s guide

3 Fitting Data

3-12

the line get reduced weight. Points that are farther from the line than would

be expected by random chance get zero weight.

For most cases, the bisquare weight scheme is preferred over LAR because it

simultaneously seeks to find a curve that fits the bulk of the data using the

usual least squares approach, and it minimizes the effect of outliers.

Robust fitting with bisquare weights uses an iteratively reweighted least

squares algorithm, and follows this procedure:

1 Fit the model by weighted least squares.

2 Compute the adjusted residuals and standardize them. The adjusted

residuals are given by

are the usual least squares residuals and h

are leverages that adjust the

residuals by downweighting high-leverage data points, which have a large

effect on the least squares fit. The standardized adjusted residuals are given

K is a tuning constant equal to 4.685, and s is the robust variance given by

MAD/0.6745 where MAD is the median absolute deviation of the residuals.

Refer to [7] for a detailed description of h, K, and s.

3 Compute the robust weights as a function of u. The bisquare weights are

given by

Note that if you supply your own regression weight vector, the final weight

is the product of the robust weight and the regression weight.

adj

1 h

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adj

----------=

1( u

()

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