Title: On higher order moment and cumulant estimation
Authors: Chunxue Li - The Chinese University of Hong Kong (Hong Kong) [presenting]
Chun Yip Yau - Chinese University of Hong Kong (Hong Kong)
Kun Chen - Southwestern University of Finance and Economics (China)
Lok Hang Chan - The Chinese University of Hong Kong (Hong Kong)
Chung Wang Wong - The Chinese University of Hong Kong (Hong Kong)
Abstract: Moments and cumulants are fundamental in statistical analysis. Particularly, many models designed for longitudinal data require estimation for higher order moments. A natural and popular approach to moment and cumulant estimation is based on sample average. However, these sample average estimators may perform poorly. We derive uniformly minimum variance unbiased estimators for raw moments, centered moments, and cumulants of any order. Explicit formulas of the estimators are obtained for a number of common distributions. Extensive simulation studies demonstrate that the proposed estimators can perform much better than the corresponding sample average estimators.