Outlier detection in nonlinear least-square regression

On a weekend project I was dealing with fitting a multivariate non-linear kinetic rate regression highly sensitive to outliers. Normally people select those points by hand, and my automation mind thought how good is it to do it by "machine". Generally I looked at two methods that are widely used, I) generalized ESD test (Rosner, 1983), and II) Robust regression and Outlier removal (ROUT) methods used in Prism/Graphpad software (Motulsky and Brown, 2006). So here I start with ESD, which was easier to implement, and maybe in future I try out ROUT.

Intro

The generalized (extreme Studentized deviate) ESD test is used to detect one or more outliers in a univariate data set that follows an approximately normal distribution (Rosner, 1983). It is an easy to use method which all it requires is to set a maximum number of outlier candidates and a significance threshold.

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