Confidence intervals from local minimums of objective function

  • Azzouz Dermoune Université of Lille 1
  • Daoud Ounaissi ESA, Angers
  • Yousri Slaoui université de Poitiers
Keywords: Gaussian model, Least absolute deviation, daily infection, Simplex algorithm, Nelder-Mead, Optim function


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


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How to Cite
Dermoune, A., Ounaissi, D., & Slaoui, Y. (2023). Confidence intervals from local minimums of objective function. Statistics, Optimization & Information Computing, 11(4), 798-810.
Research Articles