Almost Sure Convergence of Quantile-Based Estimators

Here, we investigate in more detail the quantile-based problem, cf. (1.11), especially the so far unexamined almost sure convergence, cf. Table 1.2. Note, that the whole chapter grounds on the results of Klein and Werner (2023c). The research question at hand is similar to the previous one but now applied to the empirical quantile estimator \(\widehat{q}_{\alpha ,N_1}^{X+\epsilon _{N_2}}\) .