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Seminar on Probability and Statistics
Seminar information archive ～05/20｜Next seminar｜Future seminars 05/21～
| Organizer(s) | Nakahiro Yoshida, Hiroki Masuda, Teppei Ogihara, Yuta Koike |
|---|
2025/05/13
13:30-14:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Takeshi Emura (School of Informatics and Data Science, Hiroshima University)
Change point estimation for Gaussian and binomial time series data with copula-based Markov chain models (Japanese)
https://u-tokyo-ac-jp.zoom.us/meeting/register/5OvWlB-9SMu4HiB6Zzy5Fw
Takeshi Emura (School of Informatics and Data Science, Hiroshima University)
Change point estimation for Gaussian and binomial time series data with copula-based Markov chain models (Japanese)
[ Abstract ]
Estimation of a change point is a classical statistical problem in sequential analysis and process control.
The classical maximum likelihood estimators (MLEs) for a change point are limited to independent observations or linearly dependent observations. If these conditions are violated, the MLEs substantially lose their efficiency, and a likelihood function provides a poor fit to the data. A novel change point estimator is proposed under a copula-based Markov chain model for serially dependent observations, where the marginal distribution is binomial or Gaussian. The main novelty is the adaptation of a three-state copula model, consisting of the in-control state, out-of-control state, and transition state. Under this model, a MLE is proposed with the aid of profile likelihood.
A parametric bootstrap method is adopted to compute a confidence set for the unknown change point. The simulation studies show that the proposed MLE is more efficient than the existing estimators when serial dependence in observations are specified by the model. The proposed method is illustrated by the jewelry manufacturing data and the financial crisis data. This is joint work with Prof. Li‑Hsien Sun from National Central University, Taiwan. The presentation is based on two papers:
Emura T, Lai CC, Sun LH (2023) Change point estimation under a copula-based Markov chain model for binomial time series, Econ Stat 28:120-37
Sun LH, Wang YK, Liu LH, Emura T, Chiu CY (2025) Change point estimation for Gaussian time series data with copula-based Markov chain models, Comp Stat, 40:1541–81
[ Reference URL ]Estimation of a change point is a classical statistical problem in sequential analysis and process control.
The classical maximum likelihood estimators (MLEs) for a change point are limited to independent observations or linearly dependent observations. If these conditions are violated, the MLEs substantially lose their efficiency, and a likelihood function provides a poor fit to the data. A novel change point estimator is proposed under a copula-based Markov chain model for serially dependent observations, where the marginal distribution is binomial or Gaussian. The main novelty is the adaptation of a three-state copula model, consisting of the in-control state, out-of-control state, and transition state. Under this model, a MLE is proposed with the aid of profile likelihood.
A parametric bootstrap method is adopted to compute a confidence set for the unknown change point. The simulation studies show that the proposed MLE is more efficient than the existing estimators when serial dependence in observations are specified by the model. The proposed method is illustrated by the jewelry manufacturing data and the financial crisis data. This is joint work with Prof. Li‑Hsien Sun from National Central University, Taiwan. The presentation is based on two papers:
Emura T, Lai CC, Sun LH (2023) Change point estimation under a copula-based Markov chain model for binomial time series, Econ Stat 28:120-37
Sun LH, Wang YK, Liu LH, Emura T, Chiu CY (2025) Change point estimation for Gaussian time series data with copula-based Markov chain models, Comp Stat, 40:1541–81
https://u-tokyo-ac-jp.zoom.us/meeting/register/5OvWlB-9SMu4HiB6Zzy5Fw
