How to minimize the L1 norm of residuals?

Hello,

The datasets I currently analyse are not normally distributed (according to shapiro-wilk and kolgomorov-smirnov @ p = 0.05). Therefore, I prefer plotting them as boxplots. However, I would actually like to fit a nonlinear model (in that case a dose respone curve, f(x) = y(end)./(1 + 10.^((param(1) - x)*param(2))))) to the (non-existing) mean in order to extract some parameters. So, is there any way and is it allowed to fit my function to the median instead of the mean values? I assume that I have to minimize the L1 norm of the residuals, but that gives me a hard time. Can you help me on this one?

Best regards

Philipp

Answer 1

[Matt J]

FMINSEARCH would be a good candidate, since you have only two unknowns

fun=@(param) norm( f - y(end)./(1 + 10.^((param(1) - x)*param(2)))))  ,1);

fminsearch(fun,initialGuess)