Coherent mortality forecasting by the weighted multilevel functional principal component approach

References

• K. Antonio, A. Bardoutsos and W. Ouburg, Bayesian Poisson log-bilinear models for mortality projections with multiple populations, Eur. Actuar. J. 5 (2015), pp. 245–281. doi: 10.1007/s13385-015-0115-6
   Web of Science ®Google Scholar
• P. Besse, PCA stability and choice of dimensionality, Stat. Probab. Lette. 13 (1992), pp. 405–410. doi: 10.1016/0167-7152(92)90115-L
   Web of Science ®Google Scholar
• H. Booth, J. Maindonald and L. Smith, Applying Lee-Carter under conditions of variable mortality decline, Popul. Stud. 56 (2002), pp. 325–336. doi: 10.1080/00324720215935
   Google Scholar
• D. Bosq, Linear Processes in Function Spaces: Theory and Applications, Springer, New York, 2000.
   Google Scholar
• A. Cairns, D. Blake, K. Dowd, G. Coughlan and M. Khalaf-Allah, Bayesian stochastic mortality modelling for two populations, ASTIN Bulletin 41 (2011), pp. 29–59.
   Web of Science ®Google Scholar
• C.M. Crainiceanu, A.M. Staicu and C.Z. Di, Generalized multilevel functional regression, J. Am. Stat. Assoc. 104 (2009), pp. 1550–1561. doi: 10.1198/jasa.2009.tm08564
   PubMed Web of Science ®Google Scholar
• C.Z. Di, C.M. Crainiceanu, B.S. Caffo and N.M. Punjabi, Multilevel functional principal component analysis, The Annals of Applied Statistics 3 (2009), pp. 458–488. doi: 10.1214/08-AOAS206
   PubMed Web of Science ®Google Scholar
• V. Enchev, T. Kleinow and A.J.G. Cairns, Multi-population mortality models: ftting, forecasting and comparisons, Scand. Actuar. J. 2017 (2017), pp. 319–342. doi: 10.1080/03461238.2015.1133450
   Web of Science ®Google Scholar
• J. Goldsmith, V. Zipunnikov and J. Schrack, Generalized multilevel functional-on-scalar regression and principal components analysis, Biometrics 71 (2015), pp. 344–353. doi: 10.1111/biom.12278
   PubMed Web of Science ®Google Scholar
• P. Hall, H.G. Müller and J.L. Wang, Properties of principal component methods for functional and longitudinal data analysis, Ann. Stat. 34 (2006), pp. 1493–1517. doi: 10.1214/009053606000000272
   Web of Science ®Google Scholar
• P. Hall, H.G. Müller and F. Yao, Modeling sparse generalized longitudinal observations with latent Gaussian processes, J. R. Stat. Soc. Ser. B Statist. Methodol. 70 (2008), pp. 703–723. doi: 10.1111/j.1467-9868.2008.00656.x
   Web of Science ®Google Scholar
• P. Hatzopoulos and S. Haberman, Common mortality modeling and coherent forecasts: An empirical analysis of worldwide mortality data, Insur.: Math. Econ. 52 (2013), pp. 320–337.
   Web of Science ®Google Scholar
• Human Mortality Database, Univeristy of California, Berkeley (USA), and Max Plank Institute for Demographic Research (Germany), 2010. Available at http://www.mortality.org/
   Google Scholar
• R.J. Hyndman, H. Booth and F. Yasmeen, Coherent mortality forecasting: The product-ratio method with functional time series models, Demography 50 (2013), pp. 261–283. doi: 10.1007/s13524-012-0145-5
   PubMed Web of Science ®Google Scholar
• R.J. Hyndman and Y. Khandakar, Automatic time series forecasting: The forecast package for R, J. Stat. Softw. 27 (2008), pp. 1–22. doi: 10.18637/jss.v027.i03
   Web of Science ®Google Scholar
• R.J. Hyndman and H.L. Shang, Forecasting functional time series, J. Korean Stat. Soc. 38 (2009), pp. 199–211. doi: 10.1016/j.jkss.2009.06.002
   Web of Science ®Google Scholar
• R.J. Hyndman and M.S. Ullah, Robust forecasting of mortality and fertility rates: A functional data approach, Comput. Stat. Data Anal. 51 (2007), pp. 4942–4956. doi: 10.1016/j.csda.2006.07.028
   Web of Science ®Google Scholar
• S. Jarner and E. Kryger, Modelling adult mortality in small populations: The SAINT model, ASTIN Bull. 41 (2011), pp. 377–418.
   Web of Science ®Google Scholar
• K. Karhunen, Zur spektraltheorie stochastischer prozesse, Annales Academiae Scientiarum Fennicae 37 (1946), pp. 1–37.
   Google Scholar
• T. Kleinow, A common age effect model for the mortality of multiple populations, Insur.: Math. Econ. 63 (2014), pp. 147–152.
   Web of Science ®Google Scholar
• R. Lee and L. Carter, Modeling and forecasting the time series of U.S. mortality, J. Am. Stat. Assoc. 87 (1992), pp. 659–671.
   Web of Science ®Google Scholar
• R.D. Lee and T. Miller, Evaluating the performance of the Lee-Carter method for forecasting mortality, Demography 38 (2001), pp. 537–549. doi: 10.1353/dem.2001.0036
   PubMed Web of Science ®Google Scholar
• J. Li, A Poisson common factor model for projecting mortality and life expectancy jointly for females and males, Popul Stud: J. Demography 67 (2013), pp. 111–126. doi: 10.1080/00324728.2012.689316
   PubMed Web of Science ®Google Scholar
• J. Li, L. Tickle and N. Parr, A multi-population evaluation of the Poisson common factor model for projecting mortality joint for both sexes, Journal of Population Research 33 (2016), pp. 333–360. doi: 10.1007/s12546-016-9173-0
   Web of Science ®Google Scholar
• J.S.-H. Li and M. Hardy, Measuring basis risk in longevity hedges, North Am. Actuar. J. 15 (2011), pp. 177–200. doi: 10.1080/10920277.2011.10597616
   Google Scholar
• J.S.-H. Li, R. Zhou and M. Hardy, A step-by-step guide to building two-population stochastic mortality models, Insur.: Math. Econ. 63 (2015), pp. 121–134.
   Web of Science ®Google Scholar
• N. Li and R. Lee, Coherent mortality forecasts for a group of populations: An extension of the Lee-Carter method, Demography 42 (2005), pp. 575–594. doi: 10.1353/dem.2005.0021
   PubMed Web of Science ®Google Scholar
• M. Loève, Fonctions alatoires a decomposition orthognale exponentielle, La Revue Scientifique 84 (1946), pp. 159–162.
   Google Scholar
• M.J. Meyer, B.A. Coull, F. Versace, P. Cinciripini and S.M. Jeffrey, Bayesian function-on-function regression for multilevel functional data, Biometrics 71 (2015), pp. 563–574. doi: 10.1111/biom.12299
   PubMed Web of Science ®Google Scholar
• J. Oeppen, Coherent forecasting of multiple-decrement life tables: A test using Japanese cause of death data, Technical Report, Rostock, Germany: Max Planck Institute for Demographic Research, 2008
   Google Scholar
• J.O. Ramsay and B.W. Silverman, Functional Data Analysis, Springer, New York, 2005.
   Google Scholar
• A. Renshaw and S. Haberman, Lee-Carter mortality forecasting: A parallel generalized linear modelling approach for England and Wales mortality projections, Appl. Stat. 52 (2003), pp. 119–137.
   Web of Science ®Google Scholar
• H.L. Shang, Mortality and life expectancy forecasting for a group of populations in developed countries: A multilevel functional data method, Ann. Appl. Stat. 10 (2016), pp. 1639–1672. doi: 10.1214/16-AOAS953
   Web of Science ®Google Scholar
• C. Wan and L. Bertschi, Swiss coherent mortality model as a basis for developing longevity de-risking solutions for Swiss pension funds: A practical approach, Insur.: Math. Econ. 63 (2015), pp. 66–75.
   Web of Science ®Google Scholar
• F. Yao, H.G. Müller and J.L. Wang, Functional data analysis for sparse longitudinal data, J. Am. Stat. Assoc. 100 (2005), pp. 577–590. doi: 10.1198/016214504000001745
   Web of Science ®Google Scholar
• V. Zipunnikov, B. Caffo, D.M. Yousem, C. Davatzikos, B.S. Schwartz and C. Crainiceanu, Multilevel functional principal component analysis for high-dimensional data, J. Comput. Graph. Stat. 20 (2011), pp. 852–873. doi: 10.1198/jcgs.2011.10122
   PubMed Web of Science ®Google Scholar