Statistical Details for the Robust Options
This section contains details for the Fit Robust and Fit Cauchy options in the Bivariate platform.
Fit Robust
In the Bivariate platform, the Fit Robust option reduces the influence of response variable outliers on the model fit. The Huber M-estimation method is used. Huber M-estimation finds parameter estimates that minimize the Huber loss function:
where
ei refers to the residuals
The Huber loss function penalizes outliers and increases as a quadratic for small errors and linearly for large errors. In the JMP implementation, k = 2. For more information about robust fitting, see Huber (1973) and Huber and Ronchetti (2009).
Fit Cauchy
In the Bivariate platform, the Fit Cauchy option estimates parameters using maximum likelihood and a Cauchy link function. This method assumes that the errors have a Cauchy distribution. A Cauchy distribution has fatter tails than the normal distribution, resulting in a reduced emphasis on outliers.