References
- Box, G., Jenkins, G., Reinsel, G. (1994). Time Series Analysis. Forecasting and Control (3rd ed.). Englewood Cliffs, NJ: Prentice Hall.
- Brown, P., de Jong, P. (2001). Nonparametric smoothing using state space techniques. Can. J. Stat. 29:37–50.
- Cantoni, E., Hastie, T. (2002). Degrees of freedom tests for smoothing splines. Biometrika 89:251–263.
- Carriere, J. (1992). Parametric models for life tables. Trans. Soc. Actuaries 44:77–99.
- Chandler, R., Scott, M. (2011). Statistical Methods for Trend Detection and Analysis in the Environmental Sciences ( 1st ed.). London: Wiley.
- Currie, I.D., Durban, M. (2002). Flexible smoothing with P-splines: A unified approach. Stat. Modell. 4:333–349.
- Eilers, P., Marx, B. (1996). Flexible smoothing with B-splines and penalties. Stat. Sci. 11:89–121.
- Fledelius, P., Guillen, M., Jens, P., Petersen, K. (2004). A comparative study of parametric and non-parametric estimators of old-age mortality in Sweden. J. Actuarial Pract. 11:101–126.
- Guerrero, V.M. (2007). Time series smoothing by penalized least squares. Stat. Probab. Lett. 77:1225–1234.
- Guerrero, V.M. (2008). Estimating trends with percentage of smoothness chosen by the user. Int. Stat. Rev. 76:187–202.
- Guerrero, V.M., Silva, E. (2010). Non-parametric and structured graduation of mortality rates. Popul. Rev. 49:13–26.
- Helligman, L., Pollard, J. (1980). The age pattern of mortality. J. Inst. Actuaries 107:49–80.
- Hodrick, R., Prescott, E. (1997). Post-war U.S. business cycles: An empirical investigation. J. Money, Credit and Banking 29:1–16.
- Lee, R., Carter, L. (1992). Modeling and forecasting U.S. mortality. J. Am. Stat. Assoc. 87:659–675.
- Leser, C. (1961). A simple method of trend construction. J. R. Stat. Soc., Ser.B 23:91–107.
- London, D. (1985). GRADUATION: The Revision of Estimates. Winsted, CT: ACTEX.
- Hastie, T., Tibshirani, R. (1999). Generalized Additive Models. London: Chapman & Hall.
- Hurvich, C., Simonoff, J.S., Tsai, C.L. (1998). Smoothing parameter selection in nonparametric regression using an improved Akaike information criterion. J. R. Stat. Soc. Ser.B 60:271–293.
- Kaiser, R., Maravall, A. (2001). Measuring Business Cycles in Economic Time Series. Lecture Notes in Statistics 154. New York: Springer.
- Kauermann, G. (2005). A note on smoothing parameter selection for penalized spline smoothing. J. Stat. Plann. Inference 127:53–69.
- Kitagawa, G., Gersch, W. (1996). Smoothness Priors Analysis of Time Series. Lecture Notes in Statistics 116. New York: Springer.
- Stockhammar, P., Öller, L.-E. (2012). A simple heteroscedasticity removing filter. Commun. Stat.– Theory and Methods 41:281–299.
- Proietti, T. (2005). Forecasting and signal extraction with misspecified models. J. Forecasting 24:539–556.
- Ripley, B. (2013). P-spline: Penalized Smoothing Splines [R package version 1.0-16] http://cran.r-project.org/web/packages/pspline/index.html.
- Ruppert, D., Wand, M., Carroll, R. (2003). Semiparametric Regression. Cambridge: Cambridge University Press.
- Theil, H. (1963). On the use of incomplete prior information in regression analysis. J. Am. Stat. Assoc. 58:401–414.
- Thiele, P. (1871). On a mathematical formula to express the rate of mortality through the whole of life. J. Inst. Actuaries 16:313–329.
- Tuljapurkar, S., Edwards, R. (2011). Variance in death and its implications for modeling and forecasting mortality. Demogr. Res. 21:497–526.
- Wand, M. (1999). On the optimal amount of smoothing in penalised spline regression. Biometrika 86:936–940.
- Whittaker, E. (1923). On a new method of graduation. Proc. Edinburgh Math. Soc. 41:63–75.
- Whittaker, E. (1924). On the theory of graduation. Proc. R. Soc. Edinburgh 44:77–83.
- Zhang, C. (2003). Calibrating the degrees of freedom for automatic data smoothing and effective curve checking. J. Am. Stat. Assoc. 98:609–628.