Change point estimation based on copula-based Markov chain model for binomial time series data

以作者查詢圖書館館藏

、以作者查詢臺灣博碩士

、以作者查詢全國書目

、勘誤回報

、線上人數：50

、訪客IP：3.133.109.211

姓名

賴慶杰(Lai, Ching-Chieh) 查詢紙本館藏

畢業系所

統計研究所

論文名稱

(Change point estimation based on copula-based Markov chain model for binomial time series data)

相關論文

★ A control chart based on copula-based Markov time series models	★ An improved nonparametric estimator of distribution function for bivariate competing risks model
★ Estimation and model selection for left-truncated and right-censored data: Application to power transformer lifetime modeling	★ A robust change point estimator for binomial CUSUM control charts
★ Maximum likelihood estimation for double-truncation data under a special exponential family	★ A class of generalized ridge estimator for high-dimensional linear regression
★ A copula-based parametric maximum likelihood estimation for dependently left-truncated data	★ A class of Liu-type estimators based on ridge regression under multicollinearity with an application to mixture experiments
★ Dependence measures and competing risks models under the generalized Farlie-Gumbel-Morgenstern copula	★ A review and comparison of continuity correction rules: the normal approximation to the binomial distribution
★ Likelihood inference on bivariate competing risks models under the Pareto distribution	★ Parametric likelihood inference with censored survival data under the COM-Poisson cure models
★ Likelihood-based analysis of doubly-truncated data under the location-scale and AFT models	★ Copula-based Markov chain model with binomial data
★ The Weibull joint frailty-copula model for meta-analysis with semi-competing risks data	★ A general class of multivariate survival models derived from frailty and copula models: application to reliability theory

檔案

[Endnote RIS 格式]

[Bibtex 格式]

[相關文章]

[文章引用]

[完整記錄]

[館藏目錄]

[檢視]

[下載]

本電子論文使用權限為同意立即開放。
已達開放權限電子全文僅授權使用者為學術研究之目的，進行個人非營利性質之檢索、閱讀、列印。
請遵守中華民國著作權法之相關規定，切勿任意重製、散佈、改作、轉貼、播送，以免觸法。

摘要(中)

在序列分析中，改變點的偵測與估計是一典型的問題並且在品質管制中扮演重要的角色。本篇考慮了binomial CUSUM管制圖來偵測改變點。當binomial CUSUM管制圖偵測到改變點，樣本獨立的前提下最大概似估計量可用來估計改變點。然而獨立假設在品管上是存疑的。本篇我們建造了新的模型，我們將序列相關性納入考量，並利用copula-based Markov chain來描述此相關性。我們利用最大概似法求得估計量並建造我們的R套件來推廣我們的研究成果。區間估計我們用parametric bootstrap和大樣本近似兩種方法，並將兩者以模擬做比較。本篇比較了我們提出的方法與文獻中的方法並分析實務上的資料來展示我們的研究成果。

摘要(英)

Detection and estimation of a change point is a classical problem in sequential analysis, and is an important practical issue in statistical process control. This paper is concerned about the binomial CUSUM control chart for detecting a change point for attribute data, which is extensively applied to industrial process control, health care, public health surveillance, and other fields. If the binomial CUSUM chart detects a change point, a maximum likelihood estimator can be used to estimate the change point under the assumption that the observations are independent. However, the independence assumption is questionable in many applications of statistical process control. In this paper, we consider a new change point model, where the serial correlation follows a copula-based Markov chain model and the marginal distribution follows the binominal distribution. We develop algorithms for computing the maximum likelihood estimator, and implement them in our original R package. For interval estimation, we propose a parametric bootstrap procedure and an asymptotic normal approximation procedure. We compare the performance of the two interval estimation procedures by simulations. We also compare our proposed method with the existing estimators in terms of mean squared error. We analyze the jewelry manufacturing data for illustration.

關鍵字(中)

★ 馬可夫鏈

關鍵字(英)

★ Binomial time series data
★ copula
★ Markov chain
★ serial dependence
★ attribute control chart
★ parametric bootstrap

論文目次

Chapter 1 Introduction…………….……………………………………………………………………1
Chapter 2 Background………………..…………………………………………………………………3
2.1 Settings and notations……………………………………………………………………………3
2.2. Binomial CUSUM control chart………………………………………………………………...4
2.3. Maximum likelihood estimator (MLE) of change point………………………………………5
2.4. Page’s last zero estimator………………...……………………………………………………...6
2.5. Combined estimator of MLE and last zero………...……………………………………………6
Chapter 3 Proposed method………..…………………………………………………………………...7
3.1 Copula……………………………………………………………………………………………7
3.2. Proposed change point model………………………………………………………………….10
3.3. Proposed estimator for change point………………………………………………………….15
3.4. Numerical maximization and convergence issue………………………………………………17
3.5. Asymptotic normal approximation…………………………………………………………….20
3.5. Confidence set for change point………………………………………………………………22
Chapter 4 Computation and software.…………………………………………………………….......24
4.1 Arguments in the function……………………………………………………………………...24
4.2 Illustration………………………………………………………………………………………26
Chapter 5 Simulation study.……………………………………………………………………….......29
5.1 Simulation designs……………………………………………………………………………...29
5.2 Results for comparing the NR method and the nlm method……………………………………30
5.3 Sensitivity of the proposed estimator under different assumed values of .………………...30
5.4 Results of comparing the Hessian and bootstrap methods……………………………………...31
5.5 Simulation results for comparing existing methods…………………………………………….35
Chapter 6 Data Analysis…...……………………………………………………………………….......41
6.1 Jewelry data…………………………………………………………………………………….41
6.2 Finance data…………………………………………………………………………………….46
Chapter 7 Conclusion…...………………………………………………………………………….......50
Acknowledgements…...…………………………………………………………………………….......50
References.………………………….………...……………………………………………….…….......51
Appendix A……………………………………………...…………………………………….…….......53
Appendix B-1.…………………………………………...…………………………………….…….......56
Appendix B-2.…………………………………………...…………………………………….…….......63
Appendix C.……………...……………………………...…………………………………….…….......64
Appendix D.……………...……………………………...…………………………………….…….......66

參考文獻

Assareh, H., Smith, I., and Mengersen, K., 2015. Change point detection in risk adjusted control charts. Statistical Methods in Medical Reasearch 24, 747–768.
Burr, W. I., 1979. Elementary Statistical Quality Control. Dekker, New York.
Casella, G. and Berger, R. L., 2002. Statistical Inference. Duxbury, California.
Dette, H. and Wied, D. 2016. Detecting relevant changes in time series models. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 78(2), 371-394.
Duran, R. I. and Albin, S. L., 2009. Monitoring a fraction with easy and reliable settings of the false alarm rate. Quality and Reliability Engineering International 25, 1026-1043.
Efron, B. and Tibshirani, R. J., 1993. An Introduction to the Bootstrap. Chapman & Hall, London.
Emura, T. and Lin, Y. S., 2015. A comparison of normal approximation rules for attribute control charts. Quality and Reliability Enginerring International 31, 411–418.
Emura, T., Chen, Y. H., and Chen, H. Y., 2012. Survival prediction based on compound covariate under cox proportional hazard models. PLoS ONE 7(10), e47627. doi:10.1371/journal.pone.0047627.
Emura, T., Kao, F. S., and Michimae, H., 2014. An improved nonparametric estimator of sub-distribution function for bivariate competing risk models. Journal of Multivariate Analysis 132, 229-241.
Emura, T. and Ho, Y. T., 2016. A decision theoretic approach to change point estimation for binomial CUSUM control charts. Sequential Analysis 35(2), 238-253.
Emura, T. and Liao, Y. T., 2018. Critical review and comparison of continuity correction methods: the normal approximation to the binomial distribution. Communication in Statistics - Simulation and Computation 47(8), 2266-2285.
Emura, T., Long, T. H., and Sun, L. H., 2017. R routines for performing estimation and statistical process control under copula-based time series model. Communication in Statistics - Simulation and Computation 46(4), 3067-3087.
Faugeras, Olivier P., 2017. Inference for copula modeling of discrete data: a cautionary tale and some facts. Depend. Model 5(1), 121-132.
Fuh, C. D. and Mei, Y., 2008. Optimal stationary binary quantizer for decentralized quickest change detection in hidden markov models. 11th International Conference on Information Fusion, Cologne, 1-8.
Genest, C. and Nešlehová, J., 2007. A primer on copulas for count data. The Astin Bulletin 37, 475-515.
Genest, C., Nešlehová, J., and Rémillard, B., 2017. Asymptotic behavior of the empirical multilinear copula process under broad conditions. Journal of Multivariate Analysis 159, 82-110.
Genest, C. and MacKay, R. J., 1986. Copules archimédiennes et families de lois bidimensionnelles dont les marges sont données. Canadian Journal of Statistics 14(2), 145-159.
Grigg, O. A., Farewell, V. T., and Spiegelhalter, D. J., 2003. Use of risk-adjusted CUSUM and RSPRT charts for monitoring in medical contexts. Statistical Methods in Medical Research 12, 147-170.
Hawkins, D. M. and Olwell, D. H., 1998. Cumulative Sum Charts and Charting for Quality Improvement. Wiley, New York.
Higgins, J. and Green, S., 2008. Cochrance Handbook for Systematic Reviews of Interventions. Wiley, New York.
Hollander, M. and Wolfe, D. A., 1973. Nonparametric Statistical Methods. Wiley, New York.
Huang, X. W., Chen, W. R. and Emura, T., 2019. A control chart using a copula-based Markov chain for attribute data. under revision.
Huang, X. W. and Emura, T., 2019. Model diagnostic procedures for copula-based Markov chain models for statistical process control. Communication in Statistics - Simulation and Computation. doi: 10.1080/03610918.2019.1602647.
Huang, X. W., Wang, W. and Emura, T., 2020. A copula-based Markov chain model for serially dependent event times with a dependent terminal event. Japanese Journal of Statistics and Data Science. under revision.
James, W. and Stein, C., 1961. Estimation with quadratic loss. Proceedings of Fourth Berkeley Symposium on Mathematical Statistics and Probability 1, 361-379.
Khan, R. A., 2008. Distributional properties of CUSUM stopping times. Sequential Analysis 27, 420-434.
Khan, R. A. and Khan, M. K., 2004. On the use of the SPRT in determining the properties of some CUSUM procedures. Sequential Analysis 23, 355-378.
Kim, J. M., Baik, J. and Reller, M., 2019. Control charts of mean and variance using copula Markov SPC and conditional distribution by copula. Communication in Statistics - Simulation and Computation. doi: 10.1080/03610918.2018.1547404.
Knight. K., 2000. Mathematical Statistics. Chapman & Hall, New York.
Kojadinovic, I., 2017. Some copula inference procedures adapted to the presence of ties. Computational Statistics & Data Analysis 112, 24-41.
Laheetharan, A. and Wijekoon, P., 2010. Improved estimation of the population parameters when some additional information is available. Statistical Papers 51, 889-914.
Lehmann, E. L., 1975. Nonparametric: Statistical Methods Based on Ranks. Holden-Day, San Francisco.
Long, T. H. and Emura, T., 2014. A control chart using copula-based Markov chain models. Journal of the Chinese. Statistical Association 52, 466-496.
McDonald, L., 2014. Does Newton−Raphson really fail? Stat Methods Med Res 23(3), 308-311.
Montgomery, D. C., 2009. Introduction to Statistical Quality Control. Wiley, New York.
Nagaraj, N. K., 1990. Two-sided tests for change in level for correlated data. Statistical Papers 31, 181-194.
Nelsen, R. B., 2006. An Introduction to Copulas. Springer, New York.
Page, E. S., 1954. Continuous inspection schemes. Biometrika 41, 100-114.
Perry, M. B. and Pignatiello, J. J., 2008. A change point model for the location parameter of exponential family densities. IIE Transactions 40(10), 947-956.
Perry, M. B. and Pignatiello, J. J., 2005. Estimation of the change point of the process fraction nonconforming in SPC applications. Interational Journal of Reliability Quality and Safety Engineering 12(02), 95-110.
Perry, M. B., Pignatiello, J. J., and Simpson, J. R., 2007. Estimating the change point of the process fraction nonconforming with a monotonic change disturbance in SPC. Quality and Reliability Engineering Inernational 23, 327-339.
Pignatiello, J. J. and Samuel, T. R., 2000. Identifying the time of a step change in the process fraction nonconforming. Quality Engineering 13(3), 357-365.
Rossi, G., Sarto, S. D., and Marchi, M. A., 2014. New risk-adjusted Bernoulli cumulative sum chart for monitoring binary health data. Statistical Methods in Medical Reasearch. doi: 10.1177/0962280214530883.
Sklar, A., 1959. Fonctions de re′partition a′n dimensions et leurs marges. Publica-tions de l′Intitut de Statistique de l′Universit de Paris 8, 229-231.
Sun, L. H., Huang, X. W., Alqawba, M., Kim, J. M. and Emura, T., 2020. Copula-based Markov Models for Time Series-Parametric Inference and Process Control. Springer, New York.
Teng, H. W. and Fuh, C. D., 2020. Simulating false alarm probability in K-distributed sea clutter. Communication in Statistics - Simulation and Computation. doi: 10.1080/03610918.2020.1757707.
Wang, H., 2009. Comparison of p control charts for low defective rate. Computation Statistics & Data Analysis 53(12), 4210-4220.
Wald, A., 1947. Sequential Analysis. Wiley, New York.
Wetherill, G. B. and Brown, D. B., 1991. Statistical Process Control: Theory and Practice. Chapman and Hall, London.
Wencheko, E. and Wijekoon, P., 2005. Improved estimation of the mean in one-parameter exponential families with known coefficient of variation. Statistical Papers 46, 101-115.

指導教授

江村剛志(Takeshi Emura)

審核日期

2020-7-30

推文