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I know that the L2 regression (regression-based L2 loss function/least square regression) assumptions are as follows.

1- Little or no Multicollinearity between the features.

2- Homoscedasticity Assumption.

3- Normal distribution of error terms.

4- Little or No autocorrelation in the residuals.

My question is, what are the assumptions of L1 regression (regression-based L1 loss function/Mean absolute error?

Any resources/references related to my question are appreciated.

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    $\begingroup$ You might want to consult this page about assumptions for least-squares regression. Your assumption 1 is not strictly needed. Assumption 3 is only needed for calculating p-values and the like; you can get best linear unbiased estimates without it. (Your list omits the critical assumption of linearity in the predictors, but I assume that you thought that was too obvious to mention.) $\endgroup$
    – EdM
    Commented Oct 3, 2019 at 21:38
  • $\begingroup$ Dups: stats.stackexchange.com/questions/47929/…, stats.stackexchange.com/questions/41587/… $\endgroup$
    – kjetil b halvorsen ♦
    Commented Oct 3, 2019 at 21:57
  • $\begingroup$ Note that L1 regression is a special case of what is now called quantile regression $\endgroup$
    – kjetil b halvorsen ♦
    Commented Oct 3, 2019 at 21:59
  • $\begingroup$ @EdM, to be more precise: Assumption 3 is only needed for calculating p-values and the like when the central limit theorem fails to kick in (e.g. in small samples). In large samples (asymptotically), Assumption 3 is useless. $\endgroup$
    – Richard Hardy
    Commented Oct 4, 2019 at 6:46

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