An evaluation of the performance of kernel estimators for graduating mortality data

In the graduation of the age-specific mortality pattern, recent emphasis has been placed on the use of kernel regression estimators. Three such estimators are the Nadaraya-Watson, Gasser-Muller and kernel weighted local linear estimators. This paper discusses the theoretical background of each estimator and evaluates their accuracy in graduating age-specific mortality using data for France, Japan and Sweden. For comparison, we also fit the Heligman-Pollard model and its nine-parameter variant by Kostaki. The Gasser-Muller estimator is found to be superior to the two other kernel estimators in that it is both more stable and not influenced by boundary effects. Furthermore, compared with the two parametrric models, the Gasser-Muller estimator provides a more satisfactory graduation, especially at older adult ages, in terms both of smoothness and of fidelity between the observed and graduated rates.

[1]  S. Haberman,et al.  On the choice of bandwidth for kernel graduation , 1994 .

[2]  P. Sprent,et al.  Non-Parametric Regression , 1983 .

[3]  Heather Booth,et al.  Demographic forecasting: 1980 to 2005 in review , 2006 .

[4]  G. S. Watson,et al.  Smooth regression analysis , 1964 .

[5]  E. Nadaraya.  On Estimating Regression , 1964 .

[6]  S. Schwartz.  Estimation of Probability Density by an Orthogonal Series , 1967 .

[7]  M. C. Jones,et al.  Versions of Kernel-Type Regression Estimators , 1994 .

[8]  W. Härdle.  Smoothing Techniques: With Implementation in S , 1991 .

[9]  Anestis Antoniadis,et al.  Wavelet Estimators in Nonparametric Regression: A Comparative Simulation Study , 2001 .

[10]  A Kostaki.  A nine-parameter version of the Heligman-Pollard formula. , 1992, Mathematical population studies.

[11]  Paul H. C. Eilers,et al.  Smoothing and forecasting mortality rates , 2004 .

[12]  Moving weighted average graduation using kernel estimation , 1993 .

[13]  V. A. Epanechnikov.  Non-Parametric Estimation of a Multivariate Probability Density , 1969 .

[14]  James Stephen Marron,et al.  Comparison of data-driven bandwith selectors , 1988 .

[15]  A. Bowman,et al.  Applied smoothing techniques for data analysis : the kernel approach with S-plus illustrations , 1999 .

[16]  M Hartmann.  Past and recent attempts to model mortality at all ages. , 1987, Journal of official statistics.

[17]  Y. Mack,et al.  Local Properties of k-NN Regression Estimates , 1981 .

[18]  Steven Haberman.  NON-PARAMETRIC GRADUATION USING KERNEL METHODS , 1983 .

[19]  GRADUATION: SOME EXPERIMENTS WITH KERNEL METHODS , 1987 .

[20]  M. Wand,et al.  An Effective Bandwidth Selector for Local Least Squares Regression , 1995 .

[21]  B. Benjamin,et al.  Biological Aspects of Demography. , 1971 .

[22]  T. Gasser,et al.  A Flexible and Fast Method for Automatic Smoothing , 1991 .

[23]  W. Cleveland.  Robust Locally Weighted Regression and Smoothing Scatterplots , 1979 .

[24]  Rob J. Hyndman,et al.  Robust forecasting of mortality and fertility rates: A functional data approach , 2007, Comput. Stat. Data Anal..

[25]  James Stephen Marron,et al.  Choosing a Kernel Regression Estimator , 1991 .

[26]  A. D. Wilkie,et al.  On graduation by mathematical formula , 1988 .

[27]  Eva Herrmann,et al.  Local Bandwidth Choice in Kernel Regression Estimation , 1997 .

[28]  H. Müller,et al.  Estimating regression functions and their derivatives by the kernel method , 1984 .

[29]  H. Müller,et al.  Kernel estimation of regression functions , 1979 .

[30]  T. Gasser,et al.  Locally Adaptive Bandwidth Choice for Kernel Regression Estimators , 1993 .

[31]  H. Ramlau-Hansen,et al.  The choice of a kernel function in the graduation of counting process intensities , 1983 .

[32]  T. Hastie,et al.  Local Regression: Automatic Kernel Carpentry , 1993 .

[33]  J. H. Pollard,et al.  The age pattern of mortality , 1979 .

[34]  P. Gill,et al.  Algorithms for the Solution of the Nonlinear Least-Squares Problem , 1978 .

[35]  G. Gavin,et al.  Graduation by Kernel and Adaptive Kernel Methods with a Boundary Correction , 1995 .