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題名 修勻與小區域人口之研究
A Study of smoothing methods for small area population作者 金碩
Jin, Shuoh貢獻者 余清祥
Yue, Ching-Syang
金碩
Jin, Shuoh關鍵詞 小區域人口推估
死亡率模型
修勻
標準死亡比
長壽風險
Small Area Population Projection
Mortality Models
Smoothing Methods
Standard Mortality Ratio
Longevity Risk日期 2010 上傳時間 5-Sep-2013 15:13:57 (UTC+8) 摘要 由於誤差與人口數成反比，資料多寡影響統計分析的穩定性及可靠性，因此常用於推估大區域人口的方法，往往無法直接套用至縣市及其以下層級，尤其當小區域內部地理、社會或經濟的異質性偏高時，人口推估將更為棘手。本文以兩個面向對臺灣小區域人口進行探討：其一、臺灣人口結構漸趨老化，勢必牽動政府政策與資源分配，且臺灣各縣市的人口老化速度不一，有必要針對各地特性發展適當的小區域人口推估方法；其二、因為壽命延長，全球皆面臨長壽風險(Longevity Risk)的挑戰，包括政府退休金制度規劃、壽險保費釐定等，由於臺灣各地死亡率變化不盡相同，發展小區域死亡率模型也是迫切課題。 小區域推估面臨的問題大致可歸納為四個方向：「資料品質」、「地區人數」、「資料年數」與「推估年數」，資料品質有賴資料庫與制度的建立，關於後三個問題，本文引進修勻(Smoothing, Graduation)等方法來提高小區域推估及小區域死亡模型的穩定性。人口推估方面結合修勻與區塊拔靴法(Block Bootstrap)，死亡率模型的建構則將修勻加入Lee-Carter與Age-Period-Cohort模型。由於小區域人口數較少，本文透過標準死亡比(Standard Mortality Ratio)及大區域與小區域間的連貫(Coherence)，將大區域的訊息加入小區域，降低因為地區人數較少引起的震盪。 小區域推估通常可用的資料時間較短，未來推估結果的震盪也較大，本文針對需要過去幾年資料，以及未來可推估年數等因素進行研究，希冀結果可提供臺灣各地方政府的推估參考。研究發現，參考大區域訊息有穩定推估的效果，修勻有助於降低推估誤差；另外，在小區域推估中，如有過去十五年資料可獲得較可靠的推估結果，而未來推估年數盡量不超過二十年，若地區人數過少則建議合併其他區域增加資料量後再行推估；先經過修勻而得出的死亡率模型，其效果和較為複雜的連貫模型修正相當。
The population size plays a very important role in statistical estimation, and it is difficult to derive a reliable estimation for small areas. The estimation is even more difficult if the geographic and social attributes within the small areas vary widely. However, although the population aging and longevity risk are common phenomenon in the world, the problem is not the same for different countries. The aim of this study is to explore the population projection and mortality models for small areas, with the consideration of the small area’s distinguishing characteristic. The difficulties for small area population projection can be attributed into four directions: data quality, population size, number of base years, and projection horizon. The data quality is beyond the discussion of this study and the main focus shall be laid on the other three issues. The smoothing methods and coherent models will be applied to improve the stability and accuracy of small area estimation. In the study, the block bootstrap and the smoothing methods are combined to project the population to the small areas in Taiwan. Besides, the Lee-Cater and the age-period-cohort model are extended by the smoothing and coherent methods. We found that the smoothing methods can reduce the fluctuation of estimation and projection in general, and the improvement is especially noticeable for areas with smaller population sizes. To obtain a reliable population projection for small areas, we suggest using at least fifteen-year of historical data for projection and a projection horizon not more than twenty years. Also, for developing mortality models for small areas, we found that the smoothing methods have similar effects than those methods using more complicated models, such as the coherent models.參考文獻 中文部分王郁萍(2006)。台灣地區死亡率APC 模型之研究（碩士論文）。取自http://nccur.lib.nccu.edu.tw/handle/140.119/33908王慧婷(2010)。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（未出版之碩士論文）。國立政治大學，台北市。行政院經濟建設委員會人力規劃處(2010)。2010年至2060年臺灣人口推計（編號：(99)033.805）。台北市：行政院經濟建設委員會。余清祥(1997)。修勻：統計在保險的應用。台北市：雙葉書廊。郭孟坤與余清祥(2008)。電腦模擬、隨機方法與人口推估的實證研究。人口學刊，36，67-98。陳政勳與余清祥(2010)。小區域人口推估研究：臺北市、雲嘉兩縣、澎湖縣的實證分析。人口學刊，41，153-183。 歐長潤(2008)。APC模型估計方法的模擬與實證研究（碩士論文）。取自http://nccur.lib.nccu.edu.tw/handle/140.119/36928英文部分Bates, A. (2008). The development of a postcode best fit methodology for producing population estimates for different geographies. Population Trends, 133, 28-34.Bühlmann, P. (2002). Bootstraps for time series. Statistical Science, 17(1), 52-72.Cairns, A.J.G., Blake, D., Dowd K., Coughlan G.D., & Khalaf‐Allah, M. (2011). Bayesian stochastic mortality modelling for two populations. ASTIN Bulletin, 41(1), 29-59.Cannan, E. (1895). The probability of a cessation of the growth of population in England and Wales during the next century. The Economic Journal, 5(20), 505-515.Cohen, J.E. (1986). Population forecasts and confidence intervals for sweden: A comparison of model-based and empirical approaches. Demography, 23, 105-126Copas, J.B., & Haberman, S. (1983). Nonparametric graduation using kernel methods. Journal of the Institute of Actuaries, 110, 135-156.Currie, I.D. (2006). Smoothing and forecasting mortality rates with P-Splines. Speech at the Institute of Actuaries, June 2006. Retrieved from Iain Currie`s Home Page website: http://www.ma.hw.ac.uk/~iain/research/talks/Mortality.pdfCurrie, I.D., Durban, M., & Eilers, P.H.C. (2004). Smoothing and forecasting mortality rates. Statistical Modelling ,4(4), 279‐298.Denton, F. T., Feaver, C. H., & Spencer, B. G. (2005). Time series analysis and stochastic forecasting an econometric study of mortality and life expectancy. Journal of Population Economics, 18(2), 203-227.Efron, B. (1979). Bootstrap methods: another look at the Jackknife. The Annals of Statistics, 7(1), 1-26.Gompertz, B. (1825). On the nature of the function expressive of the law of human mortality and on a new mode of determining life contingencies. Philosophical Transactions of the Royal Society of London, 115, 513-585.Hall, P. (1985). Resampling a coverage pattern. Stochastic Processes Applications, 20(2), 231-246.Heligman, L., & Pollard, J.H. (1980). The age pattern of mortality. Journal of the Institute of Actuaries, 107, 49-80.Henderson, R. (1924). A new method of graduation. Transactions of the Actuarial Society of America, 25, 29-40.Henderson, R. (1925), Further remarks on graduation. Transactions of the Actuarial Society of America, 26, 52-57.Hyndman, R.J., Booth, H., & Yasmeen, F. (2011). Coherent mortality forecasting: the product-ratio method with functional time series models (Working Paper). Retrieved from Monash University Econometrics and Business Statistics website: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2011/wp1-11.pdfKanaroglou, P.S., Maoh, H.F., Newbold, B., Scott, D.M., & Paez, A. (2009). A demographic model for small area population projections: an application to the Census Metropolitan Area of Hamilton in Ontario, Canada. Environment and Planning A, 41(4), 964-979.Kimeldorf, G. S., & Jones, D. A. (1967). Bayesian graduation. Transactions of the Society of Actuaries, 19(1), 66-112.Koissi, M. C., Shaporo, A. F., & Högnäs, G. (2006). Evaluation and extending the Lee-Cater model for mortality forecasting: Bootstrap confidence interval. Insurance: Mathematics and Economics, 38(1), 1-20.Künsch, H.R. (1989). The Jackknife and the Bootstrap for general stationary observations. Annals of Statistics, 17, 1217-1261.Lawson, C.L., & Hanson, R.J. (1974). Solving least squares problems. New Jersey: Prentice-Hall, EngleWood Cliffs.Lee, R.D., & Carter, L.R. (1992). Modeling and forecasting US mortality. Journal of the American Statistical Association, 87(419), 659-671.Lee, W. (2003). A partial SMR approach to smoothing age-specific rates. Annals of Epidemiology, 13(2), 89-99.Lewis, C.D. (1982). Industrial and business forecasting methods : a practical guide to exponential smoothing and curve fitting. London: Butterworth Scientific.Li, N., & Lee, R. (2005). Coherent mortality forecasts for a group of populations: an extension of the Lee-Carter method. Demography, 42(3), 575-594.Li, N., Lee, R., & Tuljapurkar, S. (2004). Using the Lee-Carter method to forecast mortality for populations with limited data. International Statistical Review, 72(1), 19-36.Njenga, C.N., & Sherris, M. (2009). Longevity risk and the econometric analysis of mortality trends and volatility (Working Paper). Retrieved from Social Science Research Network website: http://ssrn.com/abstract=1458084Pedroza, C. (2006). A Bayesian forecasting model: predicting U.S. male mortality. Biostatistics, 7(4), 530-550. Politis, D. N., & Romano, J. P. (1994). The stationary Bootstrap. Journal of the American Statistical Association, 89, 1303-1313.Rao, J. (2003). Small area estimation. New Jersey: John Wiley & Sons Inc.Ramlan-Hansen, H. (1983). The choice of a kernel function in the graduation of counting process intensity. Scandinavian Actuarial Journal, 165-182.Rogers, A. (1995). Multiregional demography: principles, methods and extensions. London: John Wiley.Smith, S. K.(1987). Tests of forecast accuracy and bias for county population projection. Journal of the American Statistical Association, 82, 991-1003.Smith, S. K, & Sincich, T. (1990). The relationship between the length of the base period and population forecast errors. Journal of the American Statistical Association, 85, 367-375.Ugarte, M.D., Goicoa, T., Militino, A.F., & Durbán, M. (2009). Spline smoothing in small area trend estimation and forecasting. Computational Statistics and Data Analysis, 53, 3616-3629.Whittaker, E. T. (1923). On a new method of graduation. Proceedings of the Edinburgh Mathematical Society, 41, 63-75Yang, Y., Schulhofer-Wohl, S., & Land, K.C. (2007). A simulation study of the intrinsic estimator for age-period-cohort analysis. Speech at the Annual Meetings of the American Sociological Association, August 2007. Retrieved from the website: http://www.princeton.edu/~sschulho/files/YSL_apcsim.pdfYang, Y., Schulhofer-Wohl, S., Fu, W., & Land, K. (2008). The intrinsic estimator for age-periodcohort analysis: what it is and how to use it. American Journal of Sociology, 113(6), 1697-1736.Yue, C. J. (2002). Oldest-old mortality rates and the Gompertz law: a theoretical and empirical study based on four countries. Journal of Population Studies, 24, 33-57. 描述 碩士
國立政治大學
統計研究所
98354025
99資料來源 http://thesis.lib.nccu.edu.tw/record/#G0098354025 資料類型 thesis dc.contributor.advisor 余清祥 zh_TW dc.contributor.advisor Yue, Ching-Syang en_US dc.contributor.author (Authors) 金碩 zh_TW dc.contributor.author (Authors) Jin, Shuoh en_US dc.creator (作者) 金碩 zh_TW dc.creator (作者) Jin, Shuoh en_US dc.date (日期) 2010 en_US dc.date.accessioned 5-Sep-2013 15:13:57 (UTC+8) - dc.date.available 5-Sep-2013 15:13:57 (UTC+8) - dc.date.issued (上傳時間) 5-Sep-2013 15:13:57 (UTC+8) - dc.identifier (Other Identifiers) G0098354025 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/60447 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 統計研究所 zh_TW dc.description (描述) 98354025 zh_TW dc.description (描述) 99 zh_TW dc.description.abstract (摘要) 由於誤差與人口數成反比，資料多寡影響統計分析的穩定性及可靠性，因此常用於推估大區域人口的方法，往往無法直接套用至縣市及其以下層級，尤其當小區域內部地理、社會或經濟的異質性偏高時，人口推估將更為棘手。本文以兩個面向對臺灣小區域人口進行探討：其一、臺灣人口結構漸趨老化，勢必牽動政府政策與資源分配，且臺灣各縣市的人口老化速度不一，有必要針對各地特性發展適當的小區域人口推估方法；其二、因為壽命延長，全球皆面臨長壽風險(Longevity Risk)的挑戰，包括政府退休金制度規劃、壽險保費釐定等，由於臺灣各地死亡率變化不盡相同，發展小區域死亡率模型也是迫切課題。 小區域推估面臨的問題大致可歸納為四個方向：「資料品質」、「地區人數」、「資料年數」與「推估年數」，資料品質有賴資料庫與制度的建立，關於後三個問題，本文引進修勻(Smoothing, Graduation)等方法來提高小區域推估及小區域死亡模型的穩定性。人口推估方面結合修勻與區塊拔靴法(Block Bootstrap)，死亡率模型的建構則將修勻加入Lee-Carter與Age-Period-Cohort模型。由於小區域人口數較少，本文透過標準死亡比(Standard Mortality Ratio)及大區域與小區域間的連貫(Coherence)，將大區域的訊息加入小區域，降低因為地區人數較少引起的震盪。 小區域推估通常可用的資料時間較短，未來推估結果的震盪也較大，本文針對需要過去幾年資料，以及未來可推估年數等因素進行研究，希冀結果可提供臺灣各地方政府的推估參考。研究發現，參考大區域訊息有穩定推估的效果，修勻有助於降低推估誤差；另外，在小區域推估中，如有過去十五年資料可獲得較可靠的推估結果，而未來推估年數盡量不超過二十年，若地區人數過少則建議合併其他區域增加資料量後再行推估；先經過修勻而得出的死亡率模型，其效果和較為複雜的連貫模型修正相當。 zh_TW dc.description.abstract (摘要) The population size plays a very important role in statistical estimation, and it is difficult to derive a reliable estimation for small areas. The estimation is even more difficult if the geographic and social attributes within the small areas vary widely. However, although the population aging and longevity risk are common phenomenon in the world, the problem is not the same for different countries. The aim of this study is to explore the population projection and mortality models for small areas, with the consideration of the small area’s distinguishing characteristic. The difficulties for small area population projection can be attributed into four directions: data quality, population size, number of base years, and projection horizon. The data quality is beyond the discussion of this study and the main focus shall be laid on the other three issues. The smoothing methods and coherent models will be applied to improve the stability and accuracy of small area estimation. In the study, the block bootstrap and the smoothing methods are combined to project the population to the small areas in Taiwan. Besides, the Lee-Cater and the age-period-cohort model are extended by the smoothing and coherent methods. We found that the smoothing methods can reduce the fluctuation of estimation and projection in general, and the improvement is especially noticeable for areas with smaller population sizes. To obtain a reliable population projection for small areas, we suggest using at least fifteen-year of historical data for projection and a projection horizon not more than twenty years. Also, for developing mortality models for small areas, we found that the smoothing methods have similar effects than those methods using more complicated models, such as the coherent models. en_US dc.description.tableofcontents 第一章 緒論 1第一節 研究動機 1第二節 研究問題與目的 5第二章 文獻探討 10第一節 人口推估方法 10第二節 死亡率模型 12第三節 修勻方法 17第三章 資料介紹與研究方法 22第一節 資料介紹 22第二節 研究方法 23第四章 實證研究 29第一節 修勻與小區域人口推估 29第二節 修勻與死亡率模型估計 52第三節 參考其他母體的想法 64第五章 結論與建議 67第一節 結論 67第二節 後續研究建議 70參考文獻 72附錄一：小區域修勻方法 76附錄二：地區人數、資料年數與推估年數 77附錄三：修勻與Lee-Carter模型電腦模擬 81附錄四：臺灣各縣市實證分析 84 zh_TW dc.format.extent 1543049 bytes - dc.format.mimetype application/pdf - dc.language.iso en_US - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0098354025 en_US dc.subject (關鍵詞) 小區域人口推估 zh_TW dc.subject (關鍵詞) 死亡率模型 zh_TW dc.subject (關鍵詞) 修勻 zh_TW dc.subject (關鍵詞) 標準死亡比 zh_TW dc.subject (關鍵詞) 長壽風險 zh_TW dc.subject (關鍵詞) Small Area Population Projection en_US dc.subject (關鍵詞) Mortality Models en_US dc.subject (關鍵詞) Smoothing Methods en_US dc.subject (關鍵詞) Standard Mortality Ratio en_US dc.subject (關鍵詞) Longevity Risk en_US dc.title (題名) 修勻與小區域人口之研究 zh_TW dc.title (題名) A Study of smoothing methods for small area population en_US dc.type (資料類型) thesis en dc.relation.reference (參考文獻) 中文部分王郁萍(2006)。台灣地區死亡率APC 模型之研究（碩士論文）。取自http://nccur.lib.nccu.edu.tw/handle/140.119/33908王慧婷(2010)。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（未出版之碩士論文）。國立政治大學，台北市。行政院經濟建設委員會人力規劃處(2010)。2010年至2060年臺灣人口推計（編號：(99)033.805）。台北市：行政院經濟建設委員會。余清祥(1997)。修勻：統計在保險的應用。台北市：雙葉書廊。郭孟坤與余清祥(2008)。電腦模擬、隨機方法與人口推估的實證研究。人口學刊，36，67-98。陳政勳與余清祥(2010)。小區域人口推估研究：臺北市、雲嘉兩縣、澎湖縣的實證分析。人口學刊，41，153-183。 歐長潤(2008)。APC模型估計方法的模擬與實證研究（碩士論文）。取自http://nccur.lib.nccu.edu.tw/handle/140.119/36928英文部分Bates, A. (2008). The development of a postcode best fit methodology for producing population estimates for different geographies. Population Trends, 133, 28-34.Bühlmann, P. (2002). Bootstraps for time series. Statistical Science, 17(1), 52-72.Cairns, A.J.G., Blake, D., Dowd K., Coughlan G.D., & Khalaf‐Allah, M. (2011). Bayesian stochastic mortality modelling for two populations. ASTIN Bulletin, 41(1), 29-59.Cannan, E. (1895). The probability of a cessation of the growth of population in England and Wales during the next century. The Economic Journal, 5(20), 505-515.Cohen, J.E. (1986). Population forecasts and confidence intervals for sweden: A comparison of model-based and empirical approaches. Demography, 23, 105-126Copas, J.B., & Haberman, S. (1983). Nonparametric graduation using kernel methods. Journal of the Institute of Actuaries, 110, 135-156.Currie, I.D. (2006). Smoothing and forecasting mortality rates with P-Splines. Speech at the Institute of Actuaries, June 2006. Retrieved from Iain Currie`s Home Page website: http://www.ma.hw.ac.uk/~iain/research/talks/Mortality.pdfCurrie, I.D., Durban, M., & Eilers, P.H.C. (2004). Smoothing and forecasting mortality rates. Statistical Modelling ,4(4), 279‐298.Denton, F. T., Feaver, C. H., & Spencer, B. G. (2005). Time series analysis and stochastic forecasting an econometric study of mortality and life expectancy. Journal of Population Economics, 18(2), 203-227.Efron, B. (1979). Bootstrap methods: another look at the Jackknife. The Annals of Statistics, 7(1), 1-26.Gompertz, B. (1825). On the nature of the function expressive of the law of human mortality and on a new mode of determining life contingencies. Philosophical Transactions of the Royal Society of London, 115, 513-585.Hall, P. (1985). Resampling a coverage pattern. Stochastic Processes Applications, 20(2), 231-246.Heligman, L., & Pollard, J.H. (1980). The age pattern of mortality. Journal of the Institute of Actuaries, 107, 49-80.Henderson, R. 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