Assessing Method-Strategy Pairs in the R nleqslv Package: A Comparative Study

Abstract

This study presents a comparative analysis of 14 method-strategy pairs in the \R~package \nleqslv, focusing on solving complex nonlinear systems. The primary objective is to evaluate the performance of these pairs across two models using maximum likelihood estimation. Both models introduce challenges in convergence and stability, providing a rigorous test for the optimization methods. The study assesses the methods based on key metrics such as convergence speed, estimation efficiency, and robustness (i.e., sensitivity analysis) across varying simulation setups. Findings offer insights into the strengths and limitations of different optimization strategies, highlighting optimal combinations for specific scenarios involving censored data and nonlinear estimation. The study aims to guide practitioners and researchers in selecting optimal method-strategy pairs for similar statistical problems.