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研究生:李宥萱
研究生(外文):Yu-hsuan Lee
論文名稱(外文):Improved Mortality Forecasting Using Augmented Data
指導教授:鄧惠文鄧惠文引用關係
學位類別:碩士
校院名稱:國立中央大學
系所名稱:統計研究所
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:2014
畢業學年度:102
語文別:英文
論文頁數:54
中文關鍵詞:死亡率預測Lee-Carter 模型Age-Period-Cohort 模型資料補值遺失值
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死亡率的預測在制定福利政策上扮演了一個十分重要的角色。然而對於老年人口的預測現今的死亡率模型並沒有辦法處理得很好。一個典型的問題就是人口資料的遺失。以台灣為例,由於西元1998年至1997年中死亡人數只統計到94歲,其餘超過94歲的人口資料皆歸類在95+類別中,因此我們無法得知95歲以上每個年齡層真實死亡人數。有鑑於此,在這篇研究中我們提出ㄧ些補遺失值的方法。建構在兩個十分有名的模型,Lee-Carter 模型 (Lee and Carter, 1992) 和修正後的 Age-Period-Cohort 模型 (Renshaw and Haberman, 2006)。並且,我們也比較在模擬的資料與台灣真實資料在交叉驗證上的結果。

Mortality forecasting plays an essential role in designing welfare policies and pricing aged-related financial derivatives. However, most prevailing models do not perform well in mortality forecasting particularly for the elder people. Indeed, the missing mortality data for the elder people is a typical feature in developing countries, because people are shorter-lived in earlier times and hence the mortality is recorded at fewer age categories. For example, in Taiwan, the mortality is recorded up to an age of 95 before 1997, but the mortality is recorded up to an age of 100 afterwards. This paper proposes several methods to augment the missing mortality data based on two famous models: the Lee-Carter model (Lee and Carter, 1992) and the Age-Period-Cohort model (Renshaw and Haberman, 2006). Both simulation and empirical studies demonstrate the improvement in terms of out-of-sample forecasting using a suitable data augmentation technique.
摘 要 i
Abstract ii
誌謝 iii
List of Figures v
List of Tables vi
Chapter 1 Introduction 1
Chapter 2 Review on forecasting models 4
2.1 Notations 4
2.2 The Lee-Carter Model 6
2.3 The Age-Period-Cohort Model 8
Chapter 3 Methods to impute missing data 11
3.1 The toy method 11
3.2 The weighted method 12
3.3 The two-step method 13
3.4 The MLE method 14
Chapter 4 The implementation of the MLE method 16
4.1 Algorithm under the LC model 17
4.2 Algorithm under the APC model 19
Chapter 5 Simulation studies 23
5.1 Simulation data 23
Chapter 6 Empirical analysis 26
6.1 Exploratory data analysis 26
6.2 Comparisons 36
Chapter 7 Conclusion 39
References 41

Booth, H., J. Maindonald, and L. Smith (2002). Applying Lee-Carter under conditions of variable mortality decline. Population Studies 56(3), 325-336.
Butt, Z. and S. Haberman (2009). ilc: A collection of R functions for fitting a class of Lee-Carter mortality models using iterative fitting algorithms.Actuarial Research Paper No.190 .
Cairns, A. J., D. Blake, K. Dowd, G. D. Coughlan, D. Epstein, A. Ong, and I. Balevich (2007). A quantitative comparison of stochastic mortality models using data from England and Wales and the United States. North American Actuarial Journal 13, 1-35.
Hyndman, R. and M. Ullah (2007). Robust forecasting of mortality and fertility rate: A functional data approach. Computational Statistics and Data Anaysis 51, 4942-4956.
Kupper, L. L., J. M. Janis, A. Karmous, and B. G. Greenberg (1985). Statistical Age-Period-Cohort analysis: A review and critique. Journal of Chronic Diseases 811-830, 659-671.
Lee, R. and T. Miller (2001). Evaluating the performance of the Lee-Carter method for forecasting mortality. Demography 38, 537-549.
Lee, R. D. and L. R. Carter (1992). Modelling and forecasting the time series of US mortality. Journal of the American Statistical Association 87,659-671.
Renshaw, A. and S. Haberman (2006). A cohort-based extension to the Lee-Carter model for mortality reduction factors. Insurance: Mathematics and Economics 38, 556-570.
Tuljapurkar, S., N. Li, and C. Boe (2000). A universal pattern of mortality decline in G7 countries. Nature 405, 789-792.
Wilmoth, J. (1996). Mortality projections for Japan: a comparison of four methods. Health and Mortality Among Elderly Populations, 266-287.
Yang, S. S., J. C. Yue, and H. C. Huang (2010). Modeling longevity risks using a principal component approach: A comparison with existing stochastic mortality models. Insurance: Mathematics and Economics 46, 254-270.
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