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Smoothing and forecasting mortality rates. (English) Zbl 1061.62171
Summary: The prediction of future mortality rates is a problem of fundamental importance for the insurance and pensions industry. We show how the method of $$P$$-splines can be extended to the smoothing and forecasting of two-dimensional mortality tables. We use a penalized generalized linear model with Poisson errors and show how to construct regression and penalty matrices appropriate for two-dimensional modelling. An important feature of our method is that forecasting is a natural consequence of the smoothing process. We illustrate our methods with two data sets provided by the Continuous Mortality Investigation Bureau, a central body for the collection and processing of UK insurance and pensions data.

##### MSC:
 62P05 Applications of statistics to actuarial sciences and financial mathematics 91D20 Mathematical geography and demography
FITPACK
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##### References:
 [1] Aerts M, Journal of Statistical Planning and Inference 103 pp 455– (2002) · Zbl 1011.62040 [2] de Boor C, A practical guide to splines (2001) · Zbl 0987.65015 [3] Brouhns N, Insurance: Mathematics & Economics 31 pp 373– (2002) [4] Chatfield C, Proceedings of the 18th International Workshop on Statistical Modelling pp 79– [5] Clayton D, Statistics in Medicine 6 pp 469– (1987) [6] Cleveland WS, Journal of the American Statistical Association 83 pp 597– (1988) [7] Coull BA, Biometrics 57 pp 539– (2001) · Zbl 1209.62352 [8] Coull BA, Biostatistics 2 pp 337– (2001) · Zbl 1154.62388 [9] Currie ID, Statistical Modelling 2 pp 333– (2002) · Zbl 1195.62072 [10] Dierckx P, Curve and surface fitting with splines (1993) [11] Durban M, Computational Statistics 18 pp 251– (2003) · Zbl 1050.62042 [12] Eilers PHC, Statistical Science 11 pp 89– (1996) · Zbl 0955.62562 [13] Eilers PHC, Journal of Computational and Graphical Statistics 11 pp 758– (2002) [14] Eilers PHC, Chemometrics and Intelligent Laboratory Systems 66 pp 159– (2003) [15] Eilers PHC, Computational Statistics and Data Analysis (2004) [16] Gu C, Journal of the Royal Statistical Society: Series B 55 pp 353– (1993) [17] Hastie TJ, Generalized additive models (1990) [18] Hurvich CM, Journal of the Royal Statistical Society: Series B 60 pp 271– (1998) · Zbl 0909.62039 [19] Lee TCM, Computational Statistics & Data Analysis 42 pp 139– (2003) · Zbl 1429.62144 [20] Lee RD, Journal of the American Statistical Association 87 pp 659– (1992) [21] Lin X, Journal of the Royal Statistical Society: Series B 61 pp 381– (1999) · Zbl 0915.62062 [22] Marx BD, Computational Statistics & Data Analysis 28 pp 193– (1998) · Zbl 1042.62580 [23] Marx BD, Technometrics 41 pp 1– (1999) [24] Parise H, Journal of the Royal Statistical Society: Series C 50 pp 31– (2001) · Zbl 1021.62095 [25] Ruppert D, Journal of Computational and Graphical Statistics 11 pp 735– (2002) [26] Ruppert D, Australian and New Zealand Journal of Statistics 42 pp 205– (2000) [27] Schwarz G, Annals of Statistics 6 pp 461– (1978) · Zbl 0379.62005 [28] Searle SR, Matrix algebra useful for statistics (1982) [29] Wand MP, Biometrika 86 pp 936– (1999) · Zbl 0943.62034 [30] Wand MP, Computational Statistics 18 pp 223– (2003) · Zbl 1050.62049 [31] Wood SN, Journal of the Royal Statistical Society: Series B 65 pp 95– (2003) · Zbl 1063.62059 [32] Wood SN, Ecological Modelling 157 pp 157– (2002)
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