Volume 44 - Article 45 | Pages 1085–1114 Author has provided data and code for replicating results

D-splines: Estimating rate schedules using high-dimensional splines with empirical demographic penalties

By Carl Schmertmann

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References

Alexander, M. and Alkema, L. (2018). Global estimation of neonatal mortality using a Bayesian hierarchical splines regression model. Demographic Research 38(15): 335–372.

Weblink doi:10.4054/DemRes.2018.38.15
Download reference in RIS | BibTeX

Alkema, L. and New, J.R. (2014). Global estimation of child mortality using a Bayesian B-spline bias reduction model. The Annals of Applied Statistics 8(4): 2122–2149.

Weblink doi:10.1214/14-AOAS768
Download reference in RIS | BibTeX

Amemiya, T. (1985). Advanced econometrics. Cambridge: Harvard University Press.

Download reference in RIS | BibTeX

Beer, J. (2012). Smoothing and projecting age-specific probabilities of death by TOPALS. Demographic Research 27(20): 543–592.

Weblink doi:10.4054/DemRes.2012.27.20
Download reference in RIS | BibTeX

Boor, C. (1976). Splines as linear combinations of B-splines. A survey. New York: Academic Press.

Download reference in RIS | BibTeX

Boor, C. (2001). A practical guide to splines. Applied Mathematical Sciences. New York: Springer.

Download reference in RIS | BibTeX

Camarda, C. (2012). MortalitySmooth: An R package for smoothing poisson counts with P-splines. Journal of Statistical Software 50(1): 1–24.

Weblink doi:10.18637/jss.v050.i01
Download reference in RIS | BibTeX

Camarda, C.G., Eilers, P.H., and Gampe, J. (2016). Sums of smooth exponentials to decompose complex series of counts. Statistical Modelling 16(4): 279–296.

Weblink doi:10.1177/1471082X16641796
Download reference in RIS | BibTeX

Currie, I.D., Durban, M., and Eilers, P.H. (2004). Smoothing and forecasting mortality rates. Statistical Modelling 4(4): 279–298.

Weblink doi:10.1191/1471082X04st080oa
Download reference in RIS | BibTeX

Curry, H. and Schoenberg, I. (1947). On Polya frequency functions IV: The spline functions and their limits. Bulletin of the American Mathematical Society 53(11): 1114.

Download reference in RIS | BibTeX

Eilers, P.H.C. (2017). Uncommon penalties for common problems. Journal of Chemometrics 31(4): 2878.

Weblink doi:10.1002/cem.2878
Download reference in RIS | BibTeX

Eilers, P.H.C. and Marx, B.D. (1996). Flexible smoothing with B-splines and penalties. Statistical Science 11(2): 89–102.

Weblink doi:10.1214/ss/1038425655
Download reference in RIS | BibTeX

Eilers, P.H.C. and Marx, B.D. (2010). Splines, knots, and penalties. Wiley Interdisciplinary Reviews: Computational Statistics 2(6): 637–653.

Weblink doi:10.1002/wics.125
Download reference in RIS | BibTeX

Gonzaga, M.R. and Schmertmann, C.P. (2016). Estimating age-and sex-specific mortality rates for small areas with TOPALS regression: An application to Brazil in 2010. Revista Brasileira de Estudos de Populacao 33(3): 629–652.

Weblink doi:10.20947/S0102-30982016c0009
Download reference in RIS | BibTeX

Greene, W.H. (1997). Econometric analysis. Upper Saddle River: Prentice Hall.

Download reference in RIS | BibTeX

Greville, T. (1964). Numerical procedures for interpolation by spline functions. Journal of the Society for Industrial and Applied Mathematics, Series B: Numerical Analysis 1(1): 53–68.

Download reference in RIS | BibTeX

Hilton, J., Dodd, E., Forster, J.J., and Smith, P.W.F. (2019). Projecting UK mortality by using Bayesian generalized additive models. Journal of the Royal Statistical Society 68(1): 29–49 (Series C (Applied Statistics).

Weblink doi:10.1111/rssc.12299
Download reference in RIS | BibTeX

Hoem, J.M., Madien, D., Nielsen, J.L., Ohlsen, E.M., Hansen, H.O., and Rennermalm, B. (1981). Experiments in modelling recent Danish fertility curves. Demography 18(2): 231–244.

Weblink doi:10.2307/2061095
Download reference in RIS | BibTeX

Human Fertility Database. The human fertility database [electronic resource] [electronic resource]. Rostock: Max Planck Institute for Demographic Research and Vienna: Vienna Institute of Demography.

Weblink http://www.humanfertility.org/cgi-bin/main.php
Download reference in RIS | BibTeX

Human Mortality Database (2014). The human mortality database [electronic resource] [electronic resource]. Berkeley: University of California and Rostock: Max Planck Institute for Demographic Research.

Weblink http://www.mortality.org
Download reference in RIS | BibTeX

Hyndman, R.J. and Ullah, M.S. (2007). Robust forecasting of mortality and fertility rates: A functional data approach. Computational Statistics and Data Analysis 51(10): 4942–4956.

Download reference in RIS | BibTeX

Jasilioniene, A., Jdanov, D.A., Sobotka, T., Andreev, E.M., Zeman, K., Shkolnikov, V.M., Goldstein, J.R., Philipov, D., and Rodriguez, G. (2012). Methods protocol for the human fertility database. Rostock: Max Planck Intitute for Demographic Research.

Download reference in RIS | BibTeX

Jong, P. and Tickle, L. (2006). Extending Lee–Carter mortality forecasting. Mathematical Population Studies 13(1): 1–18.

Weblink doi:10.1080/08898480500452109
Download reference in RIS | BibTeX

Lee, R.D. and Carter, L.R. (1992). Modeling and forecasting U.S. mortality. Journal of the American Statistical Association 87(419): 659–671.

Weblink doi:10.1080/01621459.1992.10475265
Download reference in RIS | BibTeX

McNeill, D., Trussell, T., and Turner, J. (1977). Spline interpolation of demographic data. Demography 14(2): 245–252.

Download reference in RIS | BibTeX

Neumaier, A. (1998). Solving Ill-conditioned and singular linear systems: A tutorial on regularization. SIAM Review 40(3): 636–666.

Weblink doi:10.1137/S0036144597321909
Download reference in RIS | BibTeX

Rau, R. and Schmertmann, C.P. (2020). District-level life expectancy in Germany. Deutsches Arzteblatt International 117(29–30): 493–499.

Weblink doi:10.3238/arztebl.2020.0493
Download reference in RIS | BibTeX

Rizzi, S., Gampe, J., and Eilers, P.H.C. (2015). Efficient estimation of smooth distributions from coarsely grouped data. American Journal of Epidemiology 182(2): 138–147.

Weblink doi:10.1093/aje/kwv020
Download reference in RIS | BibTeX

Schmertmann, C.P. (2003). A system of model fertility schedules with graphically intuitive parameters. Demographic Research 9(5): 81–110.

Weblink doi:10.4054/DemRes.2003.9.5
Download reference in RIS | BibTeX

Schmertmann, C.P. (2014). Calibrated spline estimation of detailed fertility schedules from abridged data. Revista Brasileira de Estudos de Populacao 31: 291–307.

Weblink doi:10.1590/S0102-30982014000200004
Download reference in RIS | BibTeX

Schmertmann, C.P. and Gonzaga, M.R. (2018). Bayesian estimation of age-specific mortality and life expectancy for small areas with defective vital records. Demography 55(4): 1363–1388.

Weblink doi:10.1007/s13524-018-0695-2
Download reference in RIS | BibTeX

Schmertmann, C.P., Zagheni, E., Goldstein, J.R., and Myrskyla, M. (2014). Bayesian forecasting of cohort fertility. Journal of the American Statistical Association 109(506): 500–513.

Weblink doi:10.1080/01621459.2014.881738
Download reference in RIS | BibTeX

Schoenberg, I.J. (1973). Cardinal spline interpolation. Philadelphia: SIAM.

Download reference in RIS | BibTeX

Schwarz, G. (1978). Estimating the dimension of a model. Annals of Statistics 6(2): 461–464.

Download reference in RIS | BibTeX

Wilmoth, J.R., Andreev, K., Jdanov, D., Glei, D.A., Boe, C., Bubenheim, M., Philipov, D., Shkolnikov, V., and Vachon, P. (2007). Methods protocol for the human mortality database [electronic resource. Berkeley: University of California.

Download reference in RIS | BibTeX

Ye, J. (1998). On measuring and correcting the effects of data mining and model selection. Journal of the American Statistical Association 93(441): 120–131.

Weblink doi:10.1080/01621459.1998.10474094
Download reference in RIS | BibTeX