"Whether we and our politicians know it or not, Nature is party to all our deals and decisions, and she has more votes, a longer memory, and a sterner sense of justice than we do." — Wendell Berry
I’d love to see what this does in various kinds of regression. It may be possible to set up some kind of iterative regression scheme, where a normal regression with uniform weights is first done, and then the residuals are used to define a set of alternative weights via the Tukey Loss Function. Then the weighted regression is done, producing another set of residuals, and a new set of weights is defined. This should (eventually) settle down.
The Tukey loss function, also known as Tukey’s biweight function, is a loss function that is used in robust statistics. Tukey’s loss is similar to Huber loss in that it demonstrates quadratic behavior near the origin. However, it is even more insensitive to outliers because the loss incurred by large residuals is constant, rather than scaling linearly as it would for the Huber loss.
In the above, I use $latex r$ as the argument to the function to represent “residual”, while $latex c$ is a positive parameter that the user has to choose. A common choice of this parameter is $latex c = 4.685$: Reference 1 notes that this value results…
See https://wordpress.com/view/667-per-cm.net/ Retired data scientist and statistician. Now working projects in quantitative ecology and, specifically, phenology of Bryophyta and technical methods for their study.
Pat's blog
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GeoEnergy Math
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Quotes by Nikola Tesla
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Tony Seba
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In Monte Carlo We Trust
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CLIMATE ADAM
Previously from the Science news staff at the podcast of Nature (“Nature Podcast”), the journal, now on YouTube, encouraging climate action through climate comedy.
Rabett Run
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"When Did Global Warming Stop"
Doc Snow’s treatment of the denier claim that there’s been no warming for the most recent N years. (See http://hubpages.com/@doc-snow for more on him.)
Tamino's Open Mind
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The Keeling Curve
The first, and one of the best programs for creating a spatially significant long term time series of atmospheric concentrations of CO2. Started amongst great obstacles by one, smart determined guy, Charles David Keeling.
Isaac Held's blog
In the spirit of Ray Pierrehumbert’s “big ideas come from small models” in his textbook, PRINCIPLES OF PLANETARY CLIMATE, Dr Held presents quantitative essays regarding one feature or another of the Earth’s climate and weather system.