Work

Confidence intervals from local minimums of objective function

Year: 2023

Type: article

Abstract: 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 → 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) → f (a, l, s) and the surface (l, s) → 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.

Source: Statistics Optimization & Information Computing

DOI: 10.19139/soic-2310-5070-1738

Authors: Azzouz Dermoune, Daoud Ounaissi, Yousri Slaoui

Institutions: Université de Lille, Université Lille 1, École supérieure des agricultures, Université de Poitiers

Language: English

Topic: Advanced Statistical Methods and Models

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: European Commission

Awards: G1953887145, G6880236939