Confidence intervals from local minimums of objective function

The weighted median plays a central role in the least absolute deviations (LAD). We propose nonlinear regression using Our objective function $f(a, l, s)$ is non-convex with respect to parameters a, s, and such that for each fixed s minimizer of $a\to f (a, $med(x(l, s), w(l, s))$ sequence $x(l, endowed weights $w(l, (all depend on $l$, $s$). analyse compare theoretically minimizers $(a, s)\to surface $(l, s) \to (med(x(l, s)), s)$. As numerical application we fit daily infections COVID 19 China Gaussian model. derive confident interval from local minimum.