A Non-Parametric Estimator of the Probability Weighted Moments for Large Datasets
Keywords:
PWM, median-of-means, large datasets, empirical likelihood, hypothesis testAbstract
In this paper, we introduces a nonparametric median-of-means (MoM) estimator for Probability Weighted Moments (PWM) specifically designed for large datasets. Our approach draws inspiration from the data grouping method, a widely utilized technique in various domains including economics, hydrology, finance, and insurance. We establish the consistency and asymptotic normality of the
proposed estimator under reasonable assumptions regarding the increasing number of subgroups. Additionally, we present a novel approach for testing hypotheses related to Probability Weighted Moments (PWM) using the Empirical Likelihood method (EL) specifically tailored for the median. Notably, our method circumvents the need for prior estimation of the variance structure associated
with the estimator, a task that can be challenging and prone to inaccuracies. We conducted numerical simulations to assess the performance of our proposed estimator. The results clearly indicate that our estimator showcases remarkable robustness, particularly when confronted with outliers.
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