Estimation in Copula-Based Markov Models under Weibull Distributions

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：3

、訪客IP：18.218.184.214

姓名

葉俞佑(Yu-Yu Yeh) 查詢紙本館藏

畢業系所

統計研究所

論文名稱

(Estimation in Copula-Based Markov Models under Weibull Distributions)

相關論文

★ Credit Risk Illustrated under Coupled diffusions	★ The analysis of log returns using copula-based Markov models
★ Systemic risk with relative behavior	★ 在厚尾分配下的均值收斂交易策略
★ Comparison of Credit Risk in Coupled Diffusion Model and Merton′s Model	★ Estimation in copula-based Markov mixture normal model
★ 金融系統性風險的回顧分析	★ New insights on ′′A semi-parametric model for wearable sensor-based physical activity monitoring data with informative device wear"
★ A parametric model for wearable sensor-based physical activity monitoring data with informative device wear	★ Optimal Asset Allocation using Black-Litterman with Smooth Transition Model
★ VIX Index Analysis using Copula-Based Markov Chain Models	★ 使用雙重指數平滑預測模型及無母數容忍限的配對交易策略
★ Intraday Pairs Trading on Taiwan Semiconductor Companies through Mean Reverting Processes	★ Target index tracing through portfolio optimization
★ Optimal Strategies for Index Tracking with Risky Constrains	★ On the Study of Feedforward Neural Networks: an Experimental Design Approach

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)

我們提出了基於 copula 的馬可夫模型的估計問題，因為在實踐中，連續數據通常具有相關性結構。在這個項目中，我們研究了 survival-Gumbel copula，其邊際分佈是韋伯分佈。我們獲得似然函數以及最大似然估計量。另外，為了解決區間估計，我們用三個觀察 Fisher 信息矩陣估計標準誤差。在模擬研究中，通過覆蓋概率比較三種方法哪一種更適合所提出的模型。最後，在實證研究中，分析了從 2005/1/1 到 2017/1/1 的每日收盤價 VIX 及在西班牙醫院開展手術的結直腸癌患者進行說明。特別是，我們研究了 VIX 數據的兩個邊際分佈，即韋伯分佈和指數分佈。

摘要(英)

We propose the estimation problem for a copula-based Markov model since in practice, serially data often has the dependent structure. In this project, we study the survival-Gumbel copula with the marginal distribution being the Weibull distribution. The likelihood function and the maximum likelihood estimators (MLEs) are obtained. In addition, in order to solve the interval estimation, we estimate the standard errors (SEs) with the three observed Fisher information matrices. The comparison of the three methods for investigating which one is more suitable for the proposed model in terms of the coverage probability through the simulation study. Finally, in the empirical study, the daily close VIX from 2005/1/1 to 2017/1/1 and the patients with colorectal cancer who have operations in a hospital in Spain are analyzed for illustration. In particular, we study two marginal distributions for the data, which are the Weibull distribution and the exponential distribution.

關鍵字(中)

★ 馬可夫模型
★ 觀察Fisher信息矩陣
★ 韋伯分佈
★ 指數分配

關鍵字(英)

★ Markov model
★ Survival-Gumbel copula
★ observed Fisher information matrix
★ Weibull distribution
★ exponential distribution

論文目次

Contents
1 Introduction 1
2 Copula-based Markov model 3
2.1 Weibull distribution 3
2.2 Copula function 4
2.3 Model assumption 6
2.4 The likelihood function of the survival-Gumbel copula 7
2.5 Interval estimation 8
3 Simulation study 11
3.1 Simulation methods 11
3.2 Simulation results 12
4 Empirical study 23
4.1 Data description 23
4.2 Empirical result 24
4.3 Other Empirical result 28
5 Conclusion 32
Appendix 33
Reference 42

參考文獻

Reference
[1] Carter, C. K., Kohn, R. (1994) Markov chain Monte Carlo in conditionally Gaussian state space models. Biometrika, 83, 589-601.
[2] Darsow, W. F., Nguten, B., Olsen, E. T. (1992) Copulas and Markov Processes. Illinois Journal of Mathematics,36,600−642.
[3] Domma, F., Giordano, S., Francesco, P. P. (2009). Statistical modeling of temporal dependence in ﬁnancial data via a copula function. Communications in Statistics-Simulation and Computation 38:703–728.
[4] Emura, T. Long, T. H., Sun, L. H. (2017) R routines performing estimation and statistical process control under copula-based time series models. Communications in Statistics Simulation and Computation, 46(4), 3067-3087.
[5] Frees, E. W., Valadez, E. (1998) Understanding the relationships using copulas. North American Actuarial Journal, 2, 1-25.
[6] Gelman, A., Rubin, D. (1992) Inference from Iterative simulation using Multiple sequences. Statistical Science, 7, 457-473.
[7] Kim JM, Hwang SY (2017). Directional dependence via Gaussian copula beta regression model with asymmetric GARCH marginals. Communications in Statistics Simulation and Computation, 46(10), 7639-7653.
[8] Kim JM, Baik J (2018a), Anomaly detection in sensor data, The Korean Reliability Society, Journal of Applied Reliability 18(1): 20-32.42
[9] Kim JM, Baik J (2018b), Change point detection by copula conditional distributions, manuscript.
[10] Joe,H.(1997) Multivariate Models and dependence. Chapman & hall.
[11] Long, T. H., Emura, T. (2014) A control chart using copula-based Markov chain models. Journal of the Chinese Statistical Association , 52(4), 466-496.
[12] Ly, A., Marsman, M., Verhagen, A., Grasman, R., & Wagenmakers, E.-J. (2015). A tutorial on Fisher information. Journal of Mathematical Psychology, (submitted for publication).
[13] M. Kok, J. Dahlin, T. B. Scho¨n, A. Wills, Newton-based maximum likelihood estimation in nonlinear state space models, Proc. 17th IFAC Symp. Syst. Identificat., pp. 969-974, Oct. 2015.
[14] Nelsen, R. B. (2006) An Introduction to Copulas, 2nd Edition. Springer Series in Statistics, Springer-V erlag : NewY ork.
[15] P. Zangari, An improved methodology for measuring VaR, Risk Metrics Monitor, 2nd quarter, Reuters/J.P. Morgan, 7–25 (1996).
[16] R development Core Team (2014) R: a language and environment for statistical computing. Foundation for Statistical Computing, R version 3.2.1.
[17] Ross, S. M. (2006) Simulation,4th Edition. Elevier.
[18] Otilia Boldea and Jan R. Magnus (2009) Maximum likelihood estimation of the multivariate normal mixture model.43
[19] Shih-Hao Huang, Mong-Na Lo Huang, Kainam Thomas Wong, Tzu-Chiang Tseng (2015) Copula – to model multi-channel fading by correlated but arbitrary Weibull marginals, giving a closed-form outage probability of selection combining reception.
[20] Emura T, Murotani K (2015) An algorithm for estimating survival under a copula-based dependent truncation model, TEST 24(4):734-51
[21] Sun LH, Lee CS, Emura T (2018) A Bayesian inference for time series via copula based Markov chain models, Commun Stat-Siml, doi:10.1080/03610918.2018.1529241
[22] William Q. Meeker, Luis A. Escobar (1998) Statistical methods for reliability data.
[23] Gonzalez JR, Fernandez E, Moreno V, et al. (2005) Sex diﬀerences in hospital readmission among colorectal cancer patients. J Epidemiol Commun Health; 59:506–511.
[24] Rondeau V, Gonzalez JR, Mazroui Y, et al. (2015) R frailtypack: general frailty models: shared, joint and nested frailty models with prediction. CRAN, R package version 2.7.5: CRAN: The Comprehensive R Archive Network.
[25] Emura T, Long TH, Sun LH (2017), R routines for performing estimation and statistical process control under copula-based time series models, Communications in Statistics - Simulation and Computation, 46 (4): 3067-87

指導教授

孫立憲(Li-Hsien Sun)

審核日期

2019-8-19

推文