Characteristic Function in Estimation of Probability Distribution Moments

Authors: Vladimir S. Timofeev

Abstract:

In this article the problem of distributional moments estimation is considered. The new approach of moments estimation based on usage of the characteristic function is proposed. By statistical simulation technique author shows that new approach has some robust properties. For calculation of the derivatives of characteristic function there is used numerical differentiation. Obtained results confirmed that author’s idea has a certain working efficiency and it can be recommended for any statistical applications.

Keywords: Characteristic function, distributional moments, robustness, outlier, statistical estimation problem, statistical simulation.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1094219

References:

[1] P. J. Rousseeuw, and A. M. Leroy, Robust regression and outlier detection. New York: John Wiley& Sons, 1987, 334p.
[2] P. J. Rousseeuw, and K. van Driessen, Computing LTS regression for large data sets. Dept.Mathematics, University of Antwerp, 1999.21p.
[3] R. Grübel, "The length of the shorth,” Ann. Statist., vol. 16, no. 2, pp. 619-628, 1988.
[4] J. W. Tukey, and D. H. McLaughlin, "Less vulnerable confidence and significance procedures for location based on a single sample: Trimming/Winsorization,” Sankhya, Series A, vol. 25, pp. 331-352, 1963.
[5] V. S. Timofeev, and V. Iu. Shchekoldin, "On the estimation of the statistical characteristics in the analysis of multivariate objects,”
[Ob otsenivanii statisticheskikh kharakteristik pri analize mnogofaktornykh ob"ektov]. Nauchnyi vestnik NGTU – Scientific Herald of the Novosibirsk State Technical University, vol. 24, no. 3, pp. 47-58,2006.
[6] V. S. Pugachev, Probability theory and mathematical statistics
[Teoriia veroiatnostei i matematicheskaia statistika]. Moscow, Nauka Publ., 1979, 496 p.
[7] A. Feuerverger, and R.A. Mureika, "The empirical characteristic function and its applications,” The annals of statistics, vol. 5, no. 1, pp. 88-97, 1977.
[8] J. N. Lyness, and C. B. Moler, "Numerical differentiation of analytic functions,” SIAM J. Numer. Anal., vol. 4, pp. 202-210, 1967.