Almost Sure Convergence of Moment-Based Estimators

In the following, we investigate the moment-based problem, cf. (1.10), especially the so far unexamined almost sure convergence. The whole chapter is based on the results of Klein and Werner (2023b). The corresponding research question is rather easy to postulate, i.e.: Which minimal growth condition on \(N_1\) and \(N_2\) leads to an uniform almost sure convergence of \(\bar{\gamma }_{N_1,N_2}\) towards \(\gamma \) ? Furthermore, the speed of convergence will also be examined.