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    题名: 以多個國家輔助單一國家建構死亡率模型—主成分分析之應用
    Construct mortality model for a country with deficient data by multi-countries data —application of principal component analysis
    作者: 王慧婷
    贡献者: 黃泓智
    王慧婷
    关键词: 死亡率模型
    主成分分析
    Lee-Carter模型
    日期: 2009
    上传时间: 2010-12-08 01:57:18 (UTC+8)
    摘要: 對於人口數不多的國家及地區，因為樣本數較少，死亡率的震盪較大，導致死亡率的估計值較不穩定。為解決此種問題，本研究以其他國家的死亡率資料輔助台灣，建構死亡率模型。首先，以群集分析方式選擇適合輔助台灣的國家，也就是死亡率性質相近之國家，本研究建議以死亡改善率做為主要的考量；其次，以主成分分析的方式分解多個國家死亡率，以負荷做為多個國家的共有係數，分數則是隨著資料和時間改變的變數，在研究結果中，5~6個成分個數即會有不錯的配適和預測效果，以五齡組死亡率配適模型為例，成分個數為6時，男性配適Lee-Carter模型全部國家的平均MAPE為5.40%，主成分分析則為4.13%，下降幅度將近24%，而Lee-Carter模型預測的整體MAPE為14.72%，主成分分析為12.22%，下降幅度約17%，因此主成分分析模型確實有明顯改善Lee-Carter模型。

    而和台灣死亡率性質相近的國家，主要選入歐洲國家，像是奧地利、法國、愛爾蘭、挪威和西班牙，除了法國和西班牙人口數分別為六千多萬和四千多萬的國家外，其餘三個國家人口數皆不超過一千萬，這說明人口數多寡或許不是輔助小地區建構死亡率模型的唯一重點，應選取適合的國家作為輔助用途。
    參考文獻: 英文部分
    1. Akaike, H. (1973) “Information theory and an extension of the maximum likelihood principle.” Proc. 2nd International Symposium on Information Theory (Eds. B. N. Petrov and F. Csaki), 267-281, Akademiai Kiado, Budapest.
    2. Akaike, H. (1974) “A new look at the statistical model identification.” IEEE Transactions on Automatic Control, AC-19, 716-723.
    3. Akaike, H. (1978) “A Bayesian analysis of the minimum AIC procedure.” Ann. Inst. Statist. Math., 30A, 9-14.
    4. Akaike, H. (1979) “A Bayesian analysis of the minimum AIC procedure of autoregressive model fitting.” Biometrika, 66, 237-242.
    5. Bell, W.R. (1997) “Comparing and Assessing Time Series Methods for Forecasting Age-Specific Fertility and Mortality Rates.” Journal of Official Statistics, 13(3): 279-303.
    6. Bozik, J.E. and W.R. Bell (1987) “Forecasting Age Specific Fertility Using Principal Components.” Proceeding of the American Statistical Association, Social Statistics Section, 396-401.
    7. Cairns, A. J. G., D. Blake., and K. Dowd (2006) “A Two-Factor Model for Stochastic Mortality with Parameter Uncertainty: Theory and Calibration.” Journal of Risk and Insurance, 73: 687-718.
    8. Cairns, A.J.G., D. Blake , K. Dowd, G.D. Coughlan, and M. Khalaf-Allah (2010) “Bayesian Stochastic Mortality Modelling for Two Populations.” Pension Institute Discussion Paper PI-1001.
    9. Cairns, A. J.G., D. Blake, K. Dowd, G.D. Coughlan, D. Epstein, Ong, A., and I. Balevich (2007) “A quantitative comparison of stochastic mortality models using data from England and Wales and the United States.” Department of Actuarial Mathematics and Statistics, School of Mathematical and Computer Sciences.
    10. Continuous Mortality Investigation Report No.17 (1999) Institute of Actuaries and Faculty of Actuaries.
    11. Currie, I.D. (2006) “Smoothing and Forecasting Mortality Rates with P-Splines.” Paper given at the Institute of Actuaries, June 2006. http://www.ma.hw.ac.uk/~iain/research/talks.html
    12. Currie, I.D., M. Durban, and P.H.C. Eilers (2004) “Smoothing and Forecasting Mortality Rates.” Statistical Model, 4: 279-98.
    13. Dowd, K., A.J.G. Cairns, D. Blake, G.D. Coughlan, D. Epstein, and M. Khalaf-Allah (2008a) “Backtesting Stochastic Mortality Models: An Ex-Post Evaluation of Multi-Period-Ahead Density Forecasts.” Working Paper.
    14. Dowd, K., A.J.G. Cairns, D. Blake, G.D. Coughlan, D. Epstein, and M. Khalaf-Allah (2008b) “Evaluating the Goodness of Fit of Stochastic Mortality Models.” Working Paper.
    15. Jarner, S.F., and E.M. Kryger (2009) “Modelling adult mortality in small populations: The SAINT model.” Pension Institute Discussion Paper PI-0902.
    16. Lee, R.D., and L.R. Carter (1992) “Modeling and forecasting U.S. mortality”, Journal of the American Statistical Association, 87: 659-765.
    17. Lewis, C.D. (1982) “Industrial and business forecasting methods : a practical guide to exponential smoothing and curve fitting.” London: Butterworth Scientific, 1982.
    18. Li, N., and R. Lee (2005) “Coherent mortality forecasts for a group of populations: An extension of the Lee-Carter method.” Demography, 42(3): 575-594.
    19. Mitra, S., and M.L. Levin (1997) “Model the reciprocal of the survivorship function.” Mathematical and Computer Modelling. 26(6): 57-68.
    20. Njenga, C.N., and M. Sherris (2009) “Longevity Risk and the Econometric Analysis of Mortality Trends and Volatility.” Working Paper. http://ssrn.com/abstract=1458084 .
    21. Pedroza, C. (2006) “A Bayesian forecasting model: predicting U.S. male mortality.” Biostatistics, 7(4): 530-550.
    22. Reichmuth, W. and S. Sarferaz (2008) “Bayesian demographic modeling and forecasting: An application to US mortality.” SFB 649 Discussion paper 2008-052.
    23. Renshaw, A.E., and S. Haberman (2006) “A cohort-based extension to the Lee-Carter model for mortality reduction factors”, Insurance: Mathematics and Economics, 38: 556-570.
    24. Schwartz, G. (1978) “Estimating the dimension of a model.” Ann. Statist., 6, 461-464.
    25. Wei, William W. S. (1990) Time Series Analysis: Univariate and Multivariate Methods. (2nd ed.). Redwood City, CA: Addison-Wesley.
    26. Yang, Sharon S., Jack C. Yue, Hong-Chih Huang (2010) “Modeling Longevity Risks using a Principal Component Approach: A Comparison with Existing Stochastic Mortality Models”, Insurance: Mathematics and Economics, 46: 254-270.
    中文部分
    1. 余清祥(1999)。修勻：統計在保險的應用。台北：雙葉書局。
    2. 余清祥、曾奕翔(民94年3月)。Lee-Carter模型分析:台灣地區死亡率推估之研究。楊文山(主持人)，二十一世紀的臺灣人口發展：趨勢與挑戰。2005年台灣人口學會學術研討會，國立台灣大學。
    3. 陳順宇(2005)。多變量分析。四版。台北：華泰書局。
    4. 陳文琴(民97)。死亡率改善模型的探討及保險商品自然避險策略之應用。國立政治大學風險管理與保險系研究所碩士論文。台北市。
    描述: 碩士
    國立政治大學
    風險管理與保險研究所
    97358010
    98
    資料來源: http://thesis.lib.nccu.edu.tw/record/#G0097358010
    数据类型: thesis
    显示于类别:[風險管理與保險學系] 學位論文

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