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References

Published online by Cambridge University Press:  28 April 2018

Angus S. Macdonald
Affiliation:
Heriot-Watt University, Edinburgh
Stephen J. Richards
Affiliation:
Longevitas Ltd, Edinburgh
Iain D. Currie
Affiliation:
Heriot-Watt University, Edinburgh
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References

Aalen, O. O. 1975. Statistical inference for a family of counting processes. Ph.D. thesis, University of California, Berkeley.Google Scholar
Aalen, O. O. 1978. Non-parametric inference for a family of counting processes. The Annals of Statistics, 6, 701726.10.1214/aos/1176344247CrossRefGoogle Scholar
Aalen, O. O. 1987. Dynamic modelling and causality. Scandinavian Actuarial Journal, 1987, 177190.10.1080/03461238.1987.10413826CrossRefGoogle Scholar
Akaike, H. 1973. Information theory and an extension of the maximum likelihood principle. Pages 267281 of: Petrov, B. and Cźaki, F. (eds), 2nd International Symposium on Information Theory. Akademiai Kiadó, Budapest.Google Scholar
Akaike, H. 1987. Factor analysis and AIC. Psychometrica, 52, 317333.10.1007/BF02294359CrossRefGoogle Scholar
Andersen, P. K., Borgan, Ø., Gill, R. D. and Keiding, N. 1993. Statistical Models Based on Counting Processes. Springer, New York.10.1007/978-1-4612-4348-9CrossRefGoogle Scholar
Arjas, E. 1989. Survival models and martingale dynamics. Scandinavian Journal of Statistics, 16, 177225.Google Scholar
Arjas, E. and Harra, P. 1984. A marked point process approach to censored failure data with complicated covariates. Scandinavian Journal of Statistics, 11, 193209.Google Scholar
Bailey, W. G. and Haycocks, H. W. 1947. A synthesis of methods of deriving measures of decrement from observed data. Journal of the Institute of Actuaries, 73, 179212 (with discussion).CrossRefGoogle Scholar
Beard, R. E. 1959. Note on some mathematical mortality models. Pages 302311 of: Wolstenholme, G. E. W. and O’Connor, M. (eds), The Lifespan of Animals. Little, Brown, Boston.Google Scholar
Benjamin, B. and Pollard, J.H. 1980. The Analysis of Mortality and Other Actuarial Statistics. Heinemann, London.Google Scholar
Bielecki, T. R. and Rutkowski, M. 2002. Credit Risk: Modeling, Valuation and Hedging. Springer, Berlin, Heidelberg.Google Scholar
Booth, H. and Tickle, L. 2008. Mortality modelling and forecasting: A review of methods. Annals of Actuarial Science, 3(I/II), 344.10.1017/S1748499500000440CrossRefGoogle Scholar
Bowers, N. L., Gerber, H. U., Hickman, J. C., Jones, D. A. and Nesbitt, C. J. 1986. Actuarial Mathematics. Society of Actuaries, Itasca, IL.Google Scholar
Brouhns, N., Denuit, M. and Vermunt, J. K. 2002. A Poisson log-bilinear approach to the construction of projected lifetables. Insurance: Mathematics and Economics, 31 (3), 373393.Google Scholar
Cairns, A. J. G., Blake, D. and Dowd, K. 2006. A two-factor model for stochastic mortality with parameter uncertainty: Theory and calibration. Journal of Risk and Insurance, 73, 687718.10.1111/j.1539-6975.2006.00195.xCrossRefGoogle Scholar
Cairns, A. J. G., Blake, D., Dowd, K., Coughlan, G. D., Epstein, D., Ong, A. and Balevich, I. 2009. A quantitative comparison of stochastic mortality models using data from England and Wales and the United States. North American Actuarial Journal, 13 (1), 135.10.1080/10920277.2009.10597538CrossRefGoogle Scholar
Camarda, C. G. 2012. MortalitySmooth: An R package for smoothing Poisson counts with P-splines. Journal of Statistical Software, 50, 124.10.18637/jss.v050.i01CrossRefGoogle Scholar
Carstairs, V. and Morris, R. 1991. Deprivation and Health in Scotland. Aberdeen University Press, Aberdeen.Google Scholar
Collett, D. 2003. Modelling Survival Data in Medical Research, second edn. Chapman &Hall/CRC, Boca Raton, FL.Google Scholar
Conte, S. D. and de Boor, C. 1981. Elementary Numerical Analysis: An Algorithmic Approach, third edn. McGraw-Hill, New York.Google Scholar
Continuous Mortality Investigation. 1991. Continuous Mortality Investigation Report No. 12. Institute of Actuaries and Faculty of Actuaries, London.Google Scholar
Continuous Mortality Investigation. 2007. Working Paper 26: Extensions to Younger Ages of the “00” Series Pensioner Tables of Mortality. Institute of Actuaries and Faculty of Actuaries, London.Google Scholar
Cox, D. R. 1972. Regression models and life tables. Journal of the Royal Statistical Society: Series B, 24, 187220 (with discussion).10.1111/j.2517-6161.1972.tb00899.xCrossRefGoogle Scholar
Cox, D. R. and Hinkley, D. V. 1974. Theoretical Statistics. Chapman & Hall, London.10.1007/978-1-4899-2887-0CrossRefGoogle Scholar
Cox, D. R. and Miller, H. D. 1987. The Theory of Stochastic Processes. Science Paperbacks, vol. 134. Chapman & Hall, London.Google Scholar
Crowder, M. 1991. On the identifiability crisis in competing risks analysis. Scandinavian Journal of Statistics, 18, 222233.Google Scholar
Crowder, M. 2001. Classical Competing Risks. Chapman & Hall/CRC, Boca Raton, FL.10.1201/9781420035902CrossRefGoogle Scholar
Currie, I. D. 2013. Smoothing constrained generalized linear models with an application to the Lee–Carter model. Statistical Modelling, 13, 6993.10.1177/1471082X12471373CrossRefGoogle Scholar
Currie, I. D. 2016. On fitting generalized linear and non-linear models of mortality. Scandinavian Actuarial Journal, 2016, 356383.10.1080/03461238.2014.928230CrossRefGoogle Scholar
Currie, I. D., Durban, M. and Eilers, P. H. C. 2004. Smoothing and forecasting mortality rates. Statistical Modelling, 4, 279298.10.1191/1471082X04st080oaCrossRefGoogle Scholar
Delwarde, A., Denuit, M. and Eilers, P. H. C. 2007. Smoothing the Lee–Carter and Poisson log-bilinear models for mortality forecasting: A penalized likelihood approach. Statistical Modelling, 7, 2948.10.1177/1471082X0600700103CrossRefGoogle Scholar
Dickson, D. C. M., Hardy, M. R. and Waters, H. R. 2013. Actuarial Mathematics for Life Contingent Risks, second edn. Cambridge University Press, Cambridge.Google Scholar
Djeundje, V. A. B. and Currie, I. D. 2011. Smoothing dispersed counts with applications to mortality data. Annals of Actuarial Science, 5(I), 3352.CrossRefGoogle Scholar
Dobson, A. J. 2002. An Introduction to Statistical Modelling. Chapman & Hall, London.Google Scholar
Durbin, J. and Watson, G. S. 1971. Testing for serial correlation in least squares regression, III. Biometrika, 58 (1), 119.Google Scholar
Efron, B. and Tibshirani, R. J. 1993. An Introduction to the Bootstrap, first edn. Monographs on Statistics and Applied Probability, vol. 57. Chapman & Hall, London.Google Scholar
Eilers, P. H. C. and Marx, B. D. 1996. Flexible smoothing with B-splines and penalties. Statistical Science, 11, 89121.CrossRefGoogle Scholar
Feller, W. 1950. An Introduction to Probability and its Applications, third edn. Vol. 1. John Wiley & Sons, New York.Google Scholar
Fleming, T. R. and Harrington, D. P. 1991. Counting Processes and Survival Analysis. John Wiley & Sons, New York.Google Scholar
Forfar, D. O., McCutcheon, J. J. and Wilkie, A. D. 1988. On graduation by mathematical formula. Journal of the Institute of Actuaries, 115, 1149.10.1017/S0020268100042633CrossRefGoogle Scholar
Gerber, H.U. 1990. Life Insurance Mathematics. Springer, Berlin, and the Swiss Association of Actuaries, Zurich.10.1007/978-3-662-02655-7_3CrossRefGoogle Scholar
Gini, C. 1921. Measurement of inequality of incomes. The Economic Journal, 31 (121), 124126.CrossRefGoogle Scholar
Girosi, F. and King, G. 2008. Demographic Forecasting. Princeton University Press, Princeton, NJ.10.1515/9780691186788CrossRefGoogle Scholar
Gompertz, B. 1825. The nature of the function expressive of the law of human mortality. Philosophical Transactions of the Royal Society, 115, 513585.Google Scholar
Green, P. J. and Silverman, B. W. 1994. Nonparametric Regression and Generalized Linear Models: A Roughness Penalty Approach. Chapman & Hall, London.10.1007/978-1-4899-4473-3CrossRefGoogle Scholar
Greenwood, M. 1926. The natural duration of cancer. Reports on Public Health and Medical Subjects, 33, 126.Google Scholar
Hannan, E. J. and Quinn, B. G. 1979. The determination of the order of an autoregression. Journal of the Royal Statistical Society: Series B, 41, 190195.10.1111/j.2517-6161.1979.tb01072.xCrossRefGoogle Scholar
Hardy, M. R. 2006. An Introduction to Risk Measures for Actuarial Applications. Construction and Evaluation of Actuarial Models Study Note. Society of Actuaries, Schaumburg, IL, and Casualty Actuarial Society, Arlington, VA. Available online at www.casact.org/library/studynotes/hardy4.pdf.Google Scholar
Harrell, F. E. and Davis, C. E. 1982. A new distribution-free quantile estimator. Biometrika, 69, 635640.10.1093/biomet/69.3.635CrossRefGoogle Scholar
Hastie, T. J. and Tibshirani, R. J. 1990. Generalized Additive Models. Chapman & Hall, London.Google Scholar
Hattendorff, K. 1868. Das Risiko bei der Lebensversicherung. Masius Rundschau der Versicherungen, 18, 169183.Google Scholar
Haycocks, H. W. and Perks, W. 1955. Mortality and Other Investigations. Vol. 1. Cambridge University Press, Cambridge.Google Scholar
Hoem, J. M. 1969. Markov chain models in life insurance. Blätter der Deutschen Gesellschaft für Versicherungsmathematik, 9, 91107.Google Scholar
Hoem, J. M. 1988. The versatility of the Markov chain as a tool in the mathematics of life insurance. Transactions of the 23rd International Congress of Actuaries, Helsinki, S, 171202.Google Scholar
Hoem, J. M. and Aalen, O. O. 1978. Actuarial values of payment streams. Scandinavian Actuarial Journal, 1978, 3847.10.1080/03461238.1978.10414317CrossRefGoogle Scholar
Hurvich, C. M. and Tsai, C. L. 1989. Regression and time series model selection in small samples. Biometrika, 76 (2), 297307.10.1093/biomet/76.2.297CrossRefGoogle Scholar
Hyndman, R.J. and Fan, Y. 1996. Sample quantiles in statistical packages. American Statistician, 50 (4), 361365.10.1080/00031305.1996.10473566CrossRefGoogle Scholar
Kahan, W. 1965. Further remarks on reducing truncation errors. Communications of the ACM, 8 (I), 40.10.1145/363707.363723CrossRefGoogle Scholar
Kaishev, V. K., Haberman, S. and Dimitrova, S. 2009. Spline Graduation of Crude Mortality Rates for the English Life Table 16. Office for National Statistics, London. Pages 1424.Google Scholar
Kalbfleisch, J. D. and Prentice, R. L. 2002. The Statistical Analysis of Failure Time Data, second edn. John Wiley & Sons, Hoboken, NJ.10.1002/9781118032985CrossRefGoogle Scholar
Kaplan, E. L. and Meier, P. 1958. Nonparametric estimation from incomplete observations. Journal of the American Statistical Association, 53, 457481.10.1080/01621459.1958.10501452CrossRefGoogle Scholar
Karr, A. F. 1991. Point Processes and their Statistical Inference, second edn. Marcel Dekker, New York, Basel.Google Scholar
Kendall, M. G. and Stuart, A. 1973. The Advanced Theory of Statistics, third edn. Vol. 2. Griffin, London.Google Scholar
Kleinow, T. and Richards, S. J. 2016. Parameter risk in time-series mortality forecasts. Scandinavian Actuarial Journal, 2017 (9), 804828.10.1080/03461238.2016.1255655CrossRefGoogle Scholar
Lawless, J. F. 1987. Negative binomial and mixed Poisson regression. Canadian Journal of Statistics, 15, 209225.10.2307/3314912CrossRefGoogle Scholar
Lee, R. D. and Carter, L. 1992. Modeling and forecasting US mortality. Journal of the American Statistical Association, 87, 659671.Google Scholar
Li, J. S. H., Hardy, M. R. and Tan, K. S. 2009. Uncertainty in mortality forecasting: An extension to the classic Lee–Carter approach. Astin Bulletin, 39, 137164.10.2143/AST.39.1.2038060CrossRefGoogle Scholar
Macdonald, A. S. 1996. An actuarial survey of statistical models for decrement and transition data, III: Counting process models. British Actuarial Journal, 2, 703726.10.1017/S1357321700003524CrossRefGoogle Scholar
Madrigal, A., Matthews, F., Patel, D., Gaches, A. and Baxter, S. 2011. What longevity predictors should be allowed for when valuing pension scheme liabilities? British Actuarial Journal, 16 (I), 162 (with discussion).10.1017/S1357321711000018CrossRefGoogle Scholar
Makeham, W. M. 1860. On the law of mortality and the construction of annuity tables. Journal of the Institute of Actuaries and Assurance Magazine, 8, 301310.CrossRefGoogle Scholar
McCullagh, P. and Nelder, J. A. 1989. Generalized Linear Models, second edn. Monographs on Statistics and Applied Probability, vol. 37. Chapman & Hall, London.10.1007/978-1-4899-3242-6CrossRefGoogle Scholar
McCutcheon, J. J. 1985. Experiments in graduating the data for the English Life Tables (No. 14). Transactions of the Faculty of Actuaries, 40, 135147.10.1017/S0071368600009149CrossRefGoogle Scholar
McCutcheon, J. J. and Eilbeck, J. C. 1975. Experiments in the graduation of the English Life Tables (No. 13) data. Transactions of the Faculty of Actuaries, 35, 281296.10.1017/S0071368600009630CrossRefGoogle Scholar
McLoone, P. 2000. Carstairs Scores for Scottish Postcode Sectors from the 1991 Census. Public Health Research Unit, University of Glasgow, Glasgow.Google Scholar
Neill, A. 1986. Life Contingencies. Heinemann, London.Google Scholar
Nelder, J. A. and Wedderburn, R. W. M. 1972. Generalized linear models. Journal of the Royal Statistical Society: Series A, 135, Part 3, 370384.10.2307/2344614CrossRefGoogle Scholar
Nelson, W. 1958. Theory and applications of hazard plotting for censored failure times. Technometrics, 14, 945965.CrossRefGoogle Scholar
Pawitan, Y. 2001. In All Likelihood: Statistical Modelling and Inference Using Likelihood. Oxford University Press, Oxford.10.1093/oso/9780198507659.001.0001CrossRefGoogle Scholar
Perks, W. 1932. On some experiments in the graduation of mortality statistics. Journal of the Institute of Actuaries, 63, 1240.10.1017/S0020268100046680CrossRefGoogle Scholar
Perperoglou, A. and Eilers, P. H. C. 2010. Penalized regression with individual deviance effects. Computational Statistics, 25, 341361.10.1007/s00180-009-0180-xCrossRefGoogle Scholar
Philips, L. 1990. Hanging on the metaphone. Computer Language, 7 (12), 3943.Google Scholar
Prentice, R. L., Kalbfleisch, J. D., Peterson, A. V., Jr., Flournoy, N. S., Farewell, V. T. and Breslow, N. E. 1978. The analysis of failure times in the presence of competing risks. Biometrics, 34, 541554.10.2307/2530374CrossRefGoogle ScholarPubMed
Press, W. H., Teukolsky, S. A., Vetterling, W. T. and Flannery, B. P. 1986. Numerical Recipes in C++: The Art of Scientific Computing, second edn. Cambridge University Press, New York.Google Scholar
Ramlau-Hansen, H. 1988. Hattendorff’s theorem: A Markov chain and counting process approach. Scandinavian Actuarial Journal, 1988, 143156.10.1080/03461238.1988.10413845CrossRefGoogle Scholar
Renshaw, A. E. and Haberman, S. 2006. A cohort-based extension to the Lee–Carter model for mortality reduction factors. Insurance: Mathematics and Economics, 38, 556570.Google Scholar
Richards, S. J. 2008. Applying survival models to pensioner mortality data. British Actuarial Journal, 14 (II), 257326 (with discussion).10.1017/S1357321700001720CrossRefGoogle Scholar
Richards, S. J. 2009. Selected issues in modelling mortality by cause and in small populations. British Actuarial Journal, 15 (supplement), 267283.10.1017/S1357321700005602CrossRefGoogle Scholar
Richards, S. J. 2012. A handbook of parametric survival models for actuarial use. Scandinavian Actuarial Journal, 2012 (4), 233257.10.1080/03461238.2010.506688CrossRefGoogle Scholar
Richards, S. J. 2016. Mis-estimation risk: Measurement and impact. British Actuarial Journal, 21 (3), 429457.10.1017/S1357321716000040CrossRefGoogle Scholar
Richards, S. J. and Currie, I. D. 2009. Longevity risk and annuity pricing with the Lee–Carter model. British Actuarial Journal, 15 (II) No. 65, 317365 (with discussion).10.1017/S1357321700005675CrossRefGoogle Scholar
Richards, S. J. and Jones, G. L. 2004. Financial Aspects of Longevity Risk. Staple Inn Actuarial Society (SIAS), London.Google Scholar
Richards, S. J., Kirkby, J. G. and Currie, I. D. 2006. The importance of year of birth in two-dimensional mortality data. British Actuarial Journal, 12 (I), 561 (with discussion).10.1017/S1357321700004682CrossRefGoogle Scholar
Richards, S. J., Kaufhold, K. and Rosenbusch, S. 2013. Creating portfolio-specific mortality tables: A case study. European Actuarial Journal, 3 (2), 295319.10.1007/s13385-013-0076-6CrossRefGoogle Scholar
Richards, S. J., Currie, I. D. and Ritchie, G. P. 2014. A value-at-risk framework for longevity trend risk. British Actuarial Journal, 19 (1), 116167.10.1017/S1357321712000451CrossRefGoogle Scholar
Schwarz, G. E. 1978. Estimating the dimension of a model. The Annals of Statistics, 6 (2), 461464.10.1214/aos/1176344136CrossRefGoogle Scholar
Shumway, R. H. and Stoffer, D. S. 2010. Time Series Analysis and its Applications, third edn. Springer, London.Google Scholar
Spencer, J. 1904. On the graduation of the rates of sickness and mortality. Journal of the Institute of Actuaries, 38, 334343.10.1017/S0020268100008076CrossRefGoogle Scholar
Sverdrup, E. 1965. Estimates and test procedures in connection with stochastic models for deaths, recoveries and transfers between states of health. Skandinavisk Aktuaritidskrift, 48, 184211.Google Scholar
Thatcher, A.R., Kannisto, V. and Vaupel, J.W. 1998. The Force of Mortality at Ages 80 to 100. Odense University Press, Odense.Google Scholar
The Economist . 2012. The ferment of finance. Special report on financial innovation. 25 February 2012, 8.Google Scholar
Thurston, S. W., Wand, M. P. and Wiencke, J. K. 2000. Negative binomial additive models. Biometrics, 56, 139144.10.1111/j.0006-341X.2000.00139.xCrossRefGoogle ScholarPubMed
Tsiatis, A. A. 1975. A nonidentifiability aspect of the problem of competing risks. Proceedings of the National Academy of Sciences of the United States of America, 72, 2022.10.1073/pnas.72.1.20CrossRefGoogle ScholarPubMed
Turner, H. and Firth, D. 2012. Generalized non-linear models in R: An overview of the gnm package (R package version 1.0–6). Available online at http://CRAN.R-project.org/package=gnm.Google Scholar
Waters, H. R. 1984. An approach to the study of multiple state models. Journal of the Institute of Actuaries, 111, 363374.10.1017/S0020268100041731CrossRefGoogle Scholar
Wedderburn, R. W. M. 1974. Quasi-likelihood functions, generalized linear models, and the Gauss–Newton method. Biometrika, 61, 439447.Google Scholar
Whittaker, E. T. 1923. On a new method of graduation. Proceedings of the Edinburgh Mathematical Society, 41, 6375.10.1017/S0013091500077853CrossRefGoogle Scholar
Willets, R. C. 1999. Mortality in the Next Millennium. Staple Inn Actuarial Society (SIAS), London.Google Scholar
Willets, R. C. 2004. The cohort effect: Insights and explanations. British Actuarial Journal, 10, 833877.10.1017/S1357321700002762CrossRefGoogle Scholar
Williams, D. 1991. Probability with Martingales. Cambridge University Press, Cambridge.10.1017/CBO9780511813658CrossRefGoogle Scholar
Wood, S. N. 2006. Generalized Additive Models: An Introduction with R. Chapman & Hall, London.10.1201/9781420010404CrossRefGoogle Scholar

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