## 7 Overall Comments and Future Work  
On the basis of the aforementioned results, the estimation of other parameters of extreme events like the probability of exceedance of a high level or a high quantile easily follow, but will be not discussed here. The development of new estimators of \(c\equiv c_{z}\ :=\mathbb{P}(X\leq Y|Z=z)\) is a topic that deserves further study, but is also out of the scope of this paper. The interesting behaviour of the MO\({}_{p}\) and RB MO\({}_{p}\) estimators for values of \(p\) close to \(1/\xi\) and its almost non-degenerate and consistent behaviour for \(p=1/\xi\) deserves further attention, in the direction of the developments made by [PERSON], [PERSON] and [PERSON] [38], among others. Just as with complete samples, RB GM estimation provides a better solution for the estimation of parameters of rare events under random censorship. Apart from the algorithm considered herein for the estimation of the tuning parameter \((k,p)\), several other algorithms (see, among others, [PERSON], [PERSON], [PERSON] and [PERSON] [39], where R-scripts are provided) can be used and compared--a topic also out of the scope of this paper, such as the consideration of this type of RB GM estimation for a general \(\xi\in\mathbb{R}\).  
Conceptualization, M.I.G., L.H.-R., M.M.N. and H.P.; Methodology, M.I.G., L.H.-R., M.M.N. and H.P.; Software, L.H.-R., M.M.N. and H.P.; Validation, M.I.G., L.H.-R., M.M.N. and H.P.; Formal analysis, M.I.G.; Investigation, M.I.G., L.H.-R., M.M.N. and H.P.; Writing--original  
Figure 12: Sample path of \(\hat{c}_{\chi,\mu}\) and adaptive estimate \(\widetilde{c}\) for the tongue cancer data.  
Figure 13: Sample paths of \(\hat{\xi}_{X}(k)\) (**on the left**) and of \(\hat{\xi}_{Z}(k)\) (**on the right**) for the tongue cancer data.  
draft, M.I.G., L.H.-R., M.M.N. and H.P.; Writing--review and editing, M.I.G., L.H.-R., M.M.N. and H.P.; Visualization, L.H.-R., M.M.N. and H.P.; Supervision, M.I.G.; Project administration, M.I.G.; Funding acquisition, M.I.G. and L.H.-R. All authors have read and agreed to the published version of the manuscript. This work was funded by national funds through the FCT--Fundacao para a Ciencia e a Tecnologia, I.P., under the scope of the project UIDB/00006/2020 ([[https://doi.org/10.54499/UIDB/00006/2020](https://doi.org/10.54499/UIDB/00006/2020)]([https://doi.org/10.54499/UIDB/00006/2020](https://doi.org/10.54499/UIDB/00006/2020))) (CEAUL) and project UIDB/MAT/04674/2020 ([[https://doi.org/10.54499/UIDB/04674/2020](https://doi.org/10.54499/UIDB/04674/2020)]([https://doi.org/10.54499/UIDB/04674/2020](https://doi.org/10.54499/UIDB/04674/2020))) (CIMA). The first and second authors are also financed, respectively, by HiTec Cost Action CA21163 and by project 10.54499/CEECINST/00054/2018/CP1522/CT0003 ([[https://doi.org/10.54499/CEECINST/00054/2018/CP1522/CT0003](https://doi.org/10.54499/CEECINST/00054/2018/CP1522/CT0003)]([https://doi.org/10.54499/CEECINST/00054/2018/CP1522/CT0003](https://doi.org/10.54499/CEECINST/00054/2018/CP1522/CT0003))). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Data used in this article are based on simulated and open datasets and can be obtained from the corresponding author upon request. Conflicts of Interest: The authors declare no conflicts of interest. Abbreviations The following abbreviations are used in this manuscript: CDF cumulative distribution function EVI extreme value index EVI extreme value theory GEV general extreme value GM generalized means GP generalized Pareto H [PERSON] L Lehmer ML maximum likelihood MO mean of order MSE mean squared error MVRB minimum-variance reduced-bias OS order statistics PM power mean RB reduced-bias RMSE root-mean-squared error RV random variable