Advertisement

Semi-parametric Estimation of the Change-Point of Parameters of Non-gaussian Sequences by Polynomial Maximization Method

  • Serhii W. Zabolotnii
  • Zygmunt L. Warsza
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 440)

Abstract

This paper deals with application of the maximization method in the synthesis of polynomial adaptive algorithms for a posteriori estimation of the change-point of the mean value or variance of random non-Gaussian sequences. Statistical simulation shows a significant increase in the accuracy of polynomial estimates, which is achieved by taking into account the non-Gaussian character of statistical data.

Keywords

Change-point estimation Non-Gaussian sequence Stochastic polynomial Mean value Variance Cumulant coefficients 

References

  1. 1.
    Chen, J., Gupta, A.K.: Parametric Statistical Change Point Analysis, p. 273. Birkhaeuser (2012)Google Scholar
  2. 2.
    Reeves, J., Chen, J., Wang, X.L., Lund, R., Lu, Q.: A review and comparison of change point detection techniques for climate data. J. Appl. Meteorol. Climatol. 46(6), 900–915 (2007)CrossRefGoogle Scholar
  3. 3.
    Wang, Y., Wu, C., Ji, Z., Wang, B., Liang, Y.: Non-parametric change-point method for differential gene expression detection. PLoS One 6(5), e20060 (2011)CrossRefGoogle Scholar
  4. 4.
    Yamanishi, K., Takeuchi, J., Williams, G., Milne, P.: On-line unsupervised outlier detection using finite mixtures with discounting learning algorithms. In: Proceedings of the Sixth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 320–324 (2000)Google Scholar
  5. 5.
    Liu, S., Yamada, M., Collier, N., Sugiyama, M.: Change-point detection in time-series data by relative density-ratio estimation. Neural Netw. 43, 72–83 (2013)CrossRefzbMATHGoogle Scholar
  6. 6.
    Brodsky, B., Darkhovsky, B.: Nonparametric Methods in Change-Point Problems. Kluwer Academic Publishers, Dordrecht (1993)CrossRefGoogle Scholar
  7. 7.
    Lokajicek, T., Klima, K.: A first arrival identification system of acoustic emission (AE) signals by means of a higher-order statistics approach. Meas. Sci. Technol. 17, 2461–2466 (2006)CrossRefGoogle Scholar
  8. 8.
    Wang, Y.R.: The signal change-point detection using the high-order statistics of log-likelihood difference functions. In: Proceedings of IEEE Inter-national Conference on, Acoustics, Speech and Signal Processing ICASSP, pp. 4381–4384 (2008)Google Scholar
  9. 9.
    Hilas, C.S., Rekanos, I.T., Mastorocostas P.A.: Change point detection in time series using higher-order statistics: a heuristic approach. mathematical problems in engineering. Article ID 317613 (2013)Google Scholar
  10. 10.
    Kunchenko, Y.: Polynomial Parameter Estimations of Close to Gaussian Random Variables. Shaker Verlag, Aachen (2002)Google Scholar
  11. 11.
    Hinkley, D.: Inference about the change-point in a sequence of random variables. Biometrika 57(1), 1–17 (1970)CrossRefMathSciNetzbMATHGoogle Scholar
  12. 12.
    Cramér, H.: Mathematical Methods of Statistics, vol. 9. Princeton University Press (1999)Google Scholar
  13. 13.
    Zabolotnii, S.W., Warsza, Z.L.: Semi-parametric polynomial method for retrospective estimation of the change-point of parameters of non-Gaussian sequences. In: Pavese, F., et al. (eds.) Monograph Advanced Mathematical and Computational Tools in Metrology and Testing X (AMCTM X), vol. 10, Series on Advances in Mathematics for Applied Sciences vol. 86, pp. 400–408. World Scientific, Singapore (2015)Google Scholar
  14. 14.
    Zabolotnii, S.W., Warsza, Z.L.: Semi-parametric estimation of the change-point of mean value of non-Gaussian random sequences by polynomial maximization method. In: Proceedings of 13th IMEKO TC10 Workshop on Technical Diagnostics Advanced Measurement Tools in Technical Diagnostics for Systems’ Reliability and Safety, Warsaw, Poland (2014)Google Scholar
  15. 15.
    Nosek, K.: Methods of the change point detection with limitation of the form of alternatives. PhD Thesis. AGH, Krakow (2012) (in Polish)Google Scholar
  16. 16.
    Zabolotnii, S., Warsza, Z.L.: Semi-parametric polynomial modification of CUSUM algorithms for change-point detection of non-Gaussian sequences. In: Proceedings of XXI IMEKO World Congress Measurement in Research and Industry. Prague, Czech Republic, pp. 2088–2091 (2015)Google Scholar
  17. 17.
    Warsza, Z.L., Korczynski, M.J.: A new instrument enriched by type A uncertainty evaluation. In: Proceedings of 16th IMEKO TC4 Symposium in Florence. Paper no. 1181 (2008)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Cherkasy State Technological UniversityCherkasyUkraine
  2. 2.Industrial Research Institute for Automation and Measurements PIAPWarsawPoland

Personalised recommendations