ISSN 0253-2778

CN 34-1054/N

Open AccessOpen Access JUSTC Original Paper

Influence analysis of tuning parameters on the change-point estimation in CUSUM type statistics

Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2020.07.008
  • Received Date: 24 April 2020
  • Accepted Date: 16 June 2020
  • Rev Recd Date: 16 June 2020
  • Publish Date: 31 July 2020
  • Generally, the range of tuning parameters in CUSUM type change-point estimation statistic is assumed to be (0,1) in theory. But the different values of tuning parameters often lead to the different estimation results in application. Here Monte Carlo method was used to study the influence of tuning parameters on the change-point estimation based on the jump change-point model. It was found that when the jump is large, the change-point estimate is not affected by the value of tuning parameters no matter where the true location of the change-point is. However, the value of tuning parameter has a significant effect on the change-point estimate when the jump is small. Especially, when the true location of change-point is close to one of the two trails, best estimation is obtained with the tuning parameter at 0.5. When the true location of change-point is near the center of sequence, it was observed that the smaller the tuning parameter, the better the estimation. On the basis of simulation and applications, a data-driven method was proposed to select appropriate tuning parameters from a set of possible values, which makes the CUSUM type change-point estimator more robust.
    Generally, the range of tuning parameters in CUSUM type change-point estimation statistic is assumed to be (0,1) in theory. But the different values of tuning parameters often lead to the different estimation results in application. Here Monte Carlo method was used to study the influence of tuning parameters on the change-point estimation based on the jump change-point model. It was found that when the jump is large, the change-point estimate is not affected by the value of tuning parameters no matter where the true location of the change-point is. However, the value of tuning parameter has a significant effect on the change-point estimate when the jump is small. Especially, when the true location of change-point is close to one of the two trails, best estimation is obtained with the tuning parameter at 0.5. When the true location of change-point is near the center of sequence, it was observed that the smaller the tuning parameter, the better the estimation. On the basis of simulation and applications, a data-driven method was proposed to select appropriate tuning parameters from a set of possible values, which makes the CUSUM type change-point estimator more robust.
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  • [1]
    PAGE E S. Continuous inspection schemes[J]. Biometrika, 1954, 41: 100-115.
    [2]
    GIRAITIS L, LEIPUS R, SURGAILIS D. The change-point problem for dependent observations[J]. Statistical Planning and Inference, 1996, 53(3): 297-310.
    [3]
    CSORGO M, HORWLTH L. Limit Theorems in Change-Point Analysis[M]. Chichester, UK: John Wiley and Sons Ltd, 1997.
    [4]
    HORVATH L, KOKOSZKA P. The effect of long-range dependence on change-point estimators[J]. Statistical Planning and Inference, 1997, 64(1): 57-81.
    [5]
    KOKOSZKA P, LEIPUS R. Testing for parameter changes in ARCH models[J]. Lithuanian Mathematical Journal, 1999, 39(2): 182-195.
    [6]
    HARIZ S B, WYLIE J J. Rates of convergence for the change-point estimator for long-range dependent sequences[J]. Statistics and Probability Letters, 2005, 73(2): 155-164.
    [7]
    HARIZ S B , WYLIE J J, ZHANG Q. Optimal rate of convergence for nonparametric change-point estimators for nonstationary sequences[J]. The Annals of Statistics, 2007, 35(4): 1802-1826.
    [8]
    NIE W L , HARIZ S B, WYLIE J J, et al. Change-point detection for long-range dependent sequences in a general setting[J]. Nonlinear Analysis, 2009, 71(12): 2398-2405.
    [9]
    FREMDT S. Asymptotic distribution of the delay time in Page’s sequential procedure[J]. Statistical Planning and Inference, 2013, 145: 74-91.
    [10]
    CHEN Z H, HU Y J. Cumulative sum estimator for change-point in panel data[J]. Statistical Papers, 2017, 58: 707-728.
    [11]
    QIN R B, MA J J. An efficient algorithm to estimate the change in variance[J]. Economics Letters, 2018, 168:15-17.
    [12]
    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, 2019, 46(4): 664-679.
    [13]
    TAN C C, SHI X P, WU Y H. On nonparametric change point estimator based on empirical characteristic functions[J]. Science China Mathematics, 2016, 59(12): 2463-2484.
    [14]
    Federal Reserve Bank of St. Louis. Consumer price index for all urban consumers: All items in U.S. city average (CPIAUCSL)[EB/OL]. [2020-04-01]. https://fred.stlouisfed.org/series/CPIAUCSL.
    [15]
    王伟. 基于M估计的线性回归模型均值变点检测[D]. 南京:东南大学, 2011.)
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Catalog

    [1]
    PAGE E S. Continuous inspection schemes[J]. Biometrika, 1954, 41: 100-115.
    [2]
    GIRAITIS L, LEIPUS R, SURGAILIS D. The change-point problem for dependent observations[J]. Statistical Planning and Inference, 1996, 53(3): 297-310.
    [3]
    CSORGO M, HORWLTH L. Limit Theorems in Change-Point Analysis[M]. Chichester, UK: John Wiley and Sons Ltd, 1997.
    [4]
    HORVATH L, KOKOSZKA P. The effect of long-range dependence on change-point estimators[J]. Statistical Planning and Inference, 1997, 64(1): 57-81.
    [5]
    KOKOSZKA P, LEIPUS R. Testing for parameter changes in ARCH models[J]. Lithuanian Mathematical Journal, 1999, 39(2): 182-195.
    [6]
    HARIZ S B, WYLIE J J. Rates of convergence for the change-point estimator for long-range dependent sequences[J]. Statistics and Probability Letters, 2005, 73(2): 155-164.
    [7]
    HARIZ S B , WYLIE J J, ZHANG Q. Optimal rate of convergence for nonparametric change-point estimators for nonstationary sequences[J]. The Annals of Statistics, 2007, 35(4): 1802-1826.
    [8]
    NIE W L , HARIZ S B, WYLIE J J, et al. Change-point detection for long-range dependent sequences in a general setting[J]. Nonlinear Analysis, 2009, 71(12): 2398-2405.
    [9]
    FREMDT S. Asymptotic distribution of the delay time in Page’s sequential procedure[J]. Statistical Planning and Inference, 2013, 145: 74-91.
    [10]
    CHEN Z H, HU Y J. Cumulative sum estimator for change-point in panel data[J]. Statistical Papers, 2017, 58: 707-728.
    [11]
    QIN R B, MA J J. An efficient algorithm to estimate the change in variance[J]. Economics Letters, 2018, 168:15-17.
    [12]
    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, 2019, 46(4): 664-679.
    [13]
    TAN C C, SHI X P, WU Y H. On nonparametric change point estimator based on empirical characteristic functions[J]. Science China Mathematics, 2016, 59(12): 2463-2484.
    [14]
    Federal Reserve Bank of St. Louis. Consumer price index for all urban consumers: All items in U.S. city average (CPIAUCSL)[EB/OL]. [2020-04-01]. https://fred.stlouisfed.org/series/CPIAUCSL.
    [15]
    王伟. 基于M估计的线性回归模型均值变点检测[D]. 南京:东南大学, 2011.)

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