MATLAB does not have any functions that perform Quantile Regressions.
However, you can solve Quantile Regression problems using the Optimization Toolbox. One of the functions from this toolbox that can be used towards this is FMINUNC. To use this function for LAD regression, you will need to set up your problem such that sum of the absolute values of the residuals is your objective function, which needs to be minimized.
The Statistics Toolbox contains the ROBUSTFIT function that might also be useful in solving Quantile Regressions. The ROBUSTFIT function performs linear regressions. You might be able to work with or modify this function to suit your needs.
Finally, third party tools may be available. One example is the Econometrics Toolbox provided by James P. LeSage. An internet search on "econometrics toolbox James Lesage" may provide a link to the site. Please note that third party tools are not supported or maintained by MathWorks. All questions regarding these tools should be directed to the toolbox author.
