Robust estimation techniques for the tail index of the new Pareto-type distribution

The new Pareto-type distribution offers a compelling alternative to the traditional Pareto distribution for modeling heavy-tailed data. While maximum likelihood estimation is typically employed for parameter estimation in these statistical models, this approach can produce biased results due to its inherent sensitivity to outliers. In response to this issue, we first propose an efficient and robust estimator for the tail index of the new Pareto-type distribution, grounded in the probability integral transform statistic. Subsequently, we introduce and comprehensively evaluate a second robust method—the repeated median estimator. We scrutinize the asymptotic relative efficiency of these new estimators, as well as their robustness, based on the breakdown point and influence function. Both of these methodologies, besides being computationally straightforward, offer substantial protection against outliers. A series of Monte Carlo simulations is performed to compare the performances of these new estimators against several alternative methods in outlier-free and outlier-affected scenarios. To corroborate these results, we apply the new estimators to four real datasets: the net worth of the affluent in Singapore and China, the daily increment of NASDAQ-100, and the daily new cases rate of COVID-19. This empirical application effectively attests to the practical utility of our proposed estimators.