×

zbMATH — the first resource for mathematics

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
Software:
FITPACK
PDF BibTeX XML Cite
Full Text: DOI
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)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.