Small Population Bias and Sampling Effects in Stochastic Mortality Modelling

Liang Chen, Andrew John George Cairns, Torsten Kleinow

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We propose the use of parametric bootstrap methods to investigate the finite
sample distribution of the maximum likelihood estimator for the parameter vector of a stochastic mortality model. Particular emphasis is placed on the effect that the size of the underlying population has on the distribution of the MLE in finite samples, and on the dependency structure of the resulting estimator: that is, the dependencies between estimators for the age, period and cohort effects in our model. In addition, we study the distribution of a likelihood ratio test statistic where we test a null hypothesis about the true parameters in our model. Finally, we apply the LRT to the cohort effects estimated from observed mortality rates for females in England and Wales and males in Scotland.
Original languageEnglish
Pages (from-to)193-230
Number of pages38
JournalEuropean Actuarial Journal
Issue number1
Early online date23 Jan 2017
Publication statusPublished - Jul 2017


  • Small population
  • age effect
  • period effect
  • cohort effect
  • boot- strap
  • parameter uncertainty
  • systematic parameter difference
  • likelihood ratio test
  • power of test


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