Volume 44 - Article 45 | Pages 1085–1114
D-splines: Estimating rate schedules using high-dimensional splines with empirical demographic penalties
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.
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.
Amemiya, T. (1985). Advanced econometrics. Cambridge: Harvard University Press.
Beer, J. (2012). Smoothing and projecting age-specific probabilities of death by TOPALS. Demographic Research 27(20): 543–592.
Boor, C. (2001). A practical guide to splines. Applied Mathematical Sciences. New York: Springer.
Boor, C. (1976). Splines as linear combinations of B-splines. A survey. New York: Academic Press.
Camarda, C. (2012). MortalitySmooth: An R package for smoothing poisson counts with P-splines. Journal of Statistical Software 50(1): 1–24.
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.
Currie, I.D., Durban, M., and Eilers, P.H. (2004). Smoothing and forecasting mortality rates. Statistical Modelling 4(4): 279–298.
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.
Eilers, P.H.C. (2017). Uncommon penalties for common problems. Journal of Chemometrics 31(4): 2878.
Eilers, P.H.C. and Marx, B.D. (1996). Flexible smoothing with B-splines and penalties. Statistical Science 11(2): 89–102.
Eilers, P.H.C. and Marx, B.D. (2010). Splines, knots, and penalties. Wiley Interdisciplinary Reviews: Computational Statistics 2(6): 637–653.
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.
Greene, W.H. (1997). Econometric analysis. Upper Saddle River: Prentice Hall.
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.
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).
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.
Human Fertility Database. The human fertility database [electronic resource] [electronic resource]. Rostock: Max Planck Institute for Demographic Research and Vienna: Vienna Institute of Demography.
Human Mortality Database (2014). The human mortality database [electronic resource] [electronic resource]. Berkeley: University of California and Rostock: Max Planck Institute for Demographic Research.
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.
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.
Jong, P. and Tickle, L. (2006). Extending Lee–Carter mortality forecasting. Mathematical Population Studies 13(1): 1–18.
Lee, R.D. and Carter, L.R. (1992). Modeling and forecasting U.S. mortality. Journal of the American Statistical Association 87(419): 659–671.
McNeill, D., Trussell, T., and Turner, J. (1977). Spline interpolation of demographic data. Demography 14(2): 245–252.
Neumaier, A. (1998). Solving Ill-conditioned and singular linear systems: A tutorial on regularization. SIAM Review 40(3): 636–666.
Rau, R. and Schmertmann, C.P. (2020). District-level life expectancy in Germany. Deutsches Arzteblatt International 117(29–30): 493–499.
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.
Schmertmann, C.P. (2003). A system of model fertility schedules with graphically intuitive parameters. Demographic Research 9(5): 81–110.
Schmertmann, C.P. (2014). Calibrated spline estimation of detailed fertility schedules from abridged data. Revista Brasileira de Estudos de Populacao 31: 291–307.
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.
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.
Schoenberg, I.J. (1973). Cardinal spline interpolation. Philadelphia: SIAM.
Schwarz, G. (1978). Estimating the dimension of a model. Annals of Statistics 6(2): 461–464.
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.
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.