14 questions linked to/from Fast linear regression robust to outliers
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### If linear regression is related to Pearson's correlation, are there any regression techniques related to Kendall's and Spearman's correlations?

Maybe this question is naive, but: If linear regression is closely related to Pearson's correlation coefficient, are there any regression techniques closely related to Kendall's and Spearman's ...
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### Why does the L2 norm loss have a unique solution and the L1 norm loss have possibly multiple solutions?

http://www.chioka.in/differences-between-l1-and-l2-as-loss-function-and-regularization/ If you look at the top of this post, the writer mentions that L2 norm has a unique solution and L1 norm has ...
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### When would least squares be a bad idea?

If I have a regression model: $$Y = X\beta + \varepsilon$$ where $\mathbb{V}[\varepsilon] = Id \in \mathcal{R} ^{n \times n}$ and $\mathbb{E}[\varepsilon]=(0, \ldots , 0)$, when would using \$\...
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### Outlier detection using regression

Can regression be used for out lier detection. I understand that there are ways to improve a regression model by removing the outliers. But the primary aim here is not to fit a regression model but ...
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### Choice between different robust regressions in R

I'm writing a program for evaluating real estates and I don't really understand the differences between some robust regression models, that's why I don't know which one to choose. I tried ...
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### How to optimize a regression by removing 10% “worst” data points?

I would like to remove 10% of my data points (I consider them as outliers) to maximize the R squared. Is there a way to do so efficiently? I know many people suggest not to remove outliers. But in ...
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### Quantile regression vs. Li's regression: which should I use, and when?

Is there a general rule of thumb about when robust regression or quantile regression is preferred in the presence of outliers? For example, I have a dataset where the DV exhibits extreme positive ...
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### Determining more than one outlier from a data set

I have a data set of repeated observations and I am trying to determine if any of the observations are outliers. The research I've done has only shown methods that would determine if one value (...
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### Theil-Sen estimator assumptions

I found by accident the nonparametric Theil-Sen Estimator as a replacement for standard OLS linear Regression. How well does it perform with autocorrelated data, non-normal residuals and ...
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### Other ways to find line of “best” fit

The most common methods I've seen to find a line of best fit are Least Squares regression and median-median. Are there other good ways? Is there a way to minimize the absolute value difference and ...
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### What is the maximum likelihood/GLM version of least absolute deviations for robust linear regression?

Robust linear regression from minimising the absolute deviationresults in a regression line of medians conditional on covariates, instead of means using the standard least squares methodology: Is ...
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### Elastic net: dealing with wide data with outliers

Recently I was working on a dataset with ~300 observations and 1500 predictors. I used the glmnet package in R to fit an elastic net model, which gave me a cross-...