On higher-order moment and cumulant estimation

ABSTRACT Moments and cumulants are involved in statistical analysis for a wide range of fields. A natural and popular approach to moment and cumulant estimation is based on the sample average. However, it is well known that these sample estimates usually perform poorly. In this paper, we derive uniformly minimum-variance unbiased estimator for raw moment, centred moment, and cumulant of any order for a number of common distributions. Extensive simulation studies demonstrate that the proposed estimators can perform much better than the corresponding sample average estimators.

• Publication year

  2019

• Venue

  Journal of Statistical Computation and Simulation

• Publication date

  2019-12-17

• Fields of study

  Mathematics

• Identifiers
  DOI 10.1080/00949655.2019.1700987
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Equilibrium Underdiversification and the Preference for Skewness

  2007cited by this paper
• Asymptotic Theory of Statistical Inference for Time Series

  2000cited by this paper
• Appendix: probability and measure

  1997cited by this paper
• A New Graphical Tool to Detect Non-Normality

  1996cited by this paper
• On bartlett and bartlett-type corrections francisco cribari-neto

  1996cited by this paper
• Tutorial on higher-order statistics (spectra) in signal processing and system theory: theoretical results and some applications

  1991cited by this paper
• Empirical Likelihood is Bartlett-Correctable

  1991cited by this paper
• On Diversification Given Asymmetry in Returns

  1981cited by this paper
• On The Direction of Preference for Moments of Higher Order Than The Variance

  1980cited by this paper
• The Expression of $k$-Statistic $k_{11}$ in Terms of Power Sums and Sample Moments

  1959cited by this paper
• Probability and Statistics

  1959cited by this paper
• Expression of the $k$-Statistics $k_9$ and $K_{10}$ in Terms of Power Sums and Sample Moments

  1954cited by this paper
• The Theory of Unbiased Estimation

  1946cited by this paper

• Correct estimation of higher-order spectra: From theoretical challenges to practical multi-channel implementation in SignalSnap

  2026cites this paper
• Higher-Order Spectra and their Unbiased Estimation in the GPU-accelerated SignalSnap Library

  2025cites this paper
• Hierarchic Flows to Estimate and Sample High-dimensional Probabilities

  2024cites this paper
• Expectation identities from integration by parts for univariate continuous random variables with applications to high-order moments

  2022cites this paper
• The investigation of dynamical phenomena in complex

  2022cites this paper
• Dimension reduction of noisy interacting systems

  2022cites this paper
• Rare desynchronization events in power grids: on data implementation and dimensional reductions

  2022cites this paper
• Certifying Multilevel Coherence in the Motional State of a Trapped Ion

  2021cites this paper
• Method for acquiring time of flight from high aliasing signal in heat exchange fouling ultrasonic testing

  2021cites this paper
• Traffic rate network tomography with higher‐order cumulants

  2020cites this paper