Rejoinder to the discussion of "Mode-based estimation of the center of symmetry"

TL;DR

This paper is a rejoinder addressing discussions by other researchers on a previous work about mode-based estimation of symmetry centers, clarifying and defending the original methodology and findings.

Contribution

It provides a detailed response to critiques and discussions, strengthening the original paper's arguments and clarifying methodological points.

Findings

Clarifies the original methodology and its robustness

Addresses critiques to defend the validity of mode-based estimation

Enhances understanding of symmetry center estimation techniques

Abstract

Rejoinder to the discussion by Hino (2025) and Pardo-Fern\'andez (2025) of Chac\'on and Fern\'andez Serrano (2025), a special paper (with discussion) published in Annals of the Institute of Statistical Mathematics.