# Questions tagged [least-absolute-deviations]

A regression that minimizes the sum of absolute errors (instead of the sum of squared errors).

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### Comparing the robustness least absolute deviation with OLS

My professor told us that the OLS estimator can be influenced by outliers because $$\hat{\beta}_{OLS}=\text{argmin}\left\lVert y - X^T \beta\right\rVert_2^2$$ implies that the first order ...
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### Convergence of weighted regression solution to the solution of L1 regression

I have read in this paper that the weighted regression solution converges to the solution of L1 regression, for weights, $$W_i=1/|y_i-\hat y_i|$$ I worked this out but unfortunately, I lost. Could ...
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### least absolute deviation version of deming [closed]

Based on what I know, deming minimizes the sum of square of perpendicular distance to the regression line. Is there a package in R that can run regression that minimize the sum of absolute value of ...
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### Interpretation of the least absolute deviations linear regression coefficient

In linear regression of $y$ onto $x$, one finds a $\beta_0$ and $\beta_1$ minimizing $\sum \|y - (\beta_1 x + \beta_0)\|^2$. One can show that $$\beta_1 = \rho(x,y) \frac{\sigma(y)}{\sigma(x)},$$ ...
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### Can I use gradient descent for Least Absolute Deviation Regression?

I've read in some posts that the absolute function is not differentiable. However, it is not differentiable only at 0. Can I not check the value at each training point to calculate the derivative. ...
1 vote
465 views

### For syntax of least absolute deviation from package 'L1pack' [closed]

I am trying to use the least absolute deviation regression from my dataset which has one column of dependent variable and multiple columns of independent variables. I tried using the following syntax ...
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1k views

### Is it possible to force least absolute deviations (LAD) regression to return the 'median' value when infinite solutions are possible?

I have a problem where LAD regressions is not giving me a solution as the R package (L1pack) errors whenever there is an infinite number of possible solutions*. ...
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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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### Why is Coordinate Descent not used to solve Least Absolute Deviation?

I have recently been looking into why Least Absolute Deviation (LAD) is not used in place of OLS for machine learning, and it appears the primary reason is due to difficulty in computing a solution ...
1 vote
### What is the standard measure of fit quality for least absolute deviation regression (the analog of $R^2$) [duplicate]
When one runs an OLS regression, one often prefers to look at $R^2$ rather than the mean squared error, though both measure goodness of fit. $R^2$ is dimensionless and has some advantageous properties:...
### $R^2$ for least absolute deviation regression
I know that $R^2$ is for the least square regression. Is there an analogous measure of fit to $R^2$ in LAD (Least Absolute Deviations) regression? Here I am concerned with the "fitting quality".