ISSN 0253-2778

CN 34-1054/N

open
Free to Publish. Free to Read.
Open AccessOpen Access JUSTC Original Paper

Limit properties of weighted cumulative sum estimator of change-point in variance

  • Department of Statistics and Finance,School of Management, University of Science and Technology of China, Hefei 230026, China

Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2020.04.001
  • Received Date: 25 October 2019
  • Accepted Date: 20 February 2020
  • Rev Recd Date: 20 February 2020
  • Publish Date: 30 April 2020
    Abstract

  • Abstract

    Some limit properties of the weighted cumulative sum(WCS) estimator for the change-point in variance was studied. The consistency and convergence rate of the estimator were proved. In addition, the asymptotic distribution of the change-point estimator under local alternative hypothesis, which was a two-side Brownian motion with a drift, was developed. By the numerical solution of asymmetric distribution, an asymptotic confidence interval was constructed. Simulation results and a real data example show that the proposed estimator has a good performance in the application.

    Abstract

    Some limit properties of the weighted cumulative sum(WCS) estimator for the change-point in variance was studied. The consistency and convergence rate of the estimator were proved. In addition, the asymptotic distribution of the change-point estimator under local alternative hypothesis, which was a two-side Brownian motion with a drift, was developed. By the numerical solution of asymmetric distribution, an asymptotic confidence interval was constructed. Simulation results and a real data example show that the proposed estimator has a good performance in the application.
    • FullText(HTML)
  • loading
    • References(11)
  • [1]
    PAGE E S. Continuous inspection schemes[J]. Biometrika, 1954, 41: 100-115.
    [2]
    HSU D A. Tests for variance shift at an unknown time point [J]. Journal of the Royal Statistical Society: Series C (Applied Statistics), 1977, 26(3): 279-284.
    [3]
    XU M, WU Y, JIN B. Detection of a change-point in variance by a weighted sum of powers of variances test[J]. Journal of Applied Statistics, 2018, 46(4): 664-679.
    [4]
    BAI J. Least squares estimation of a shift in linear processes [J]. Journal of Time Series Analysis, 1994, 15(5):453-472.
    [5]
    JIN B, DONG C, TAN C, et al. Estimator of a change point in single index models[J]. Science China Mathematics, 2014, 57(8): 1701-1712.
    [6]
    JENSEN J L W V. Sur les fonctions convexes et les inégalités entre les valeurs moyennes[J]. Acta Mathematica, 1906, 30: 175-193.
    [7]
    BAI J. Estimation of a change point in multiple regression models[J]. Review of Economics and Statistics, 1997, 79(4): 551-563.
    [8]
    YAO Y C. Approximating the distribution of the maximum likelihood estimate of the change-point in a sequence of independent random variables[J]. The Annals of Statistics, 1987,15(3): 1321-1328.
    [9]
    PICARD D. Testing and estimating change-points in time series[J]. Advances in Applied Probability, 1985, 17(4): 841-867.
    [10]
    MANN H B, WALD A. On stochastic limit and order relationships[J]. The Annals of Mathematical Statistics, 1943, 14(3): 217-226.
    [11]
    KILLICK R, FEARNHEAD P, ECKLEY I A. Optimal detection of changepoints with a linear computational cost[J]. Journal of the American Statistical Association, 2012, 107(500): 1590-1598.)
    • Supplements(0)
    • Related Articles
    • Track Citations
  • 加载中

Catalog

    Get Citation
    PDF
    XML
    [1]
    PAGE E S. Continuous inspection schemes[J]. Biometrika, 1954, 41: 100-115.
    [2]
    HSU D A. Tests for variance shift at an unknown time point [J]. Journal of the Royal Statistical Society: Series C (Applied Statistics), 1977, 26(3): 279-284.
    [3]
    XU M, WU Y, JIN B. Detection of a change-point in variance by a weighted sum of powers of variances test[J]. Journal of Applied Statistics, 2018, 46(4): 664-679.
    [4]
    BAI J. Least squares estimation of a shift in linear processes [J]. Journal of Time Series Analysis, 1994, 15(5):453-472.
    [5]
    JIN B, DONG C, TAN C, et al. Estimator of a change point in single index models[J]. Science China Mathematics, 2014, 57(8): 1701-1712.
    [6]
    JENSEN J L W V. Sur les fonctions convexes et les inégalités entre les valeurs moyennes[J]. Acta Mathematica, 1906, 30: 175-193.
    [7]
    BAI J. Estimation of a change point in multiple regression models[J]. Review of Economics and Statistics, 1997, 79(4): 551-563.
    [8]
    YAO Y C. Approximating the distribution of the maximum likelihood estimate of the change-point in a sequence of independent random variables[J]. The Annals of Statistics, 1987,15(3): 1321-1328.
    [9]
    PICARD D. Testing and estimating change-points in time series[J]. Advances in Applied Probability, 1985, 17(4): 841-867.
    [10]
    MANN H B, WALD A. On stochastic limit and order relationships[J]. The Annals of Mathematical Statistics, 1943, 14(3): 217-226.
    [11]
    KILLICK R, FEARNHEAD P, ECKLEY I A. Optimal detection of changepoints with a linear computational cost[J]. Journal of the American Statistical Association, 2012, 107(500): 1590-1598.)
    Recommended articles
    TrendMD
    Volume 50 Issue 4 page: 389-395
    Cover

    Article Metrics

    Article views (61) PDF downloads(116)
    Proportional views

    Copyright © Editorial Office of JUSTC, All Rights Reserved. 皖ICP备05002528号

    Supported by: Beijing Renhe Information Technology Co. Ltd    

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return