Small Population Bias and Sampling Effects in Stochastic Mortality Modelling

Liang Chen; Andrew John George Cairns; Torsten Kleinow

doi:10.1007/s13385-016-0143-x

Small Population Bias and Sampling Effects in Stochastic Mortality Modelling

Liang Chen, Andrew John George Cairns, Torsten Kleinow

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Abstract

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 language	English
Pages (from-to)	193-230
Number of pages	38
Journal	European Actuarial Journal
Volume	7
Issue number	1
Early online date	23 Jan 2017
DOIs	https://doi.org/10.1007/s13385-016-0143-x
Publication status	Published - Jul 2017

Keywords

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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10.1007/s13385-016-0143-x

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Andrew John George Cairns
- A.J.G.Cairnshw.acuk
- School of Mathematical & Computer Sciences - Professor
- School of Mathematical & Computer Sciences, Actuarial Mathematics & Statistics - Professor
Person: Academic (Research & Teaching)

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title = "Small Population Bias and Sampling Effects in Stochastic Mortality Modelling",

abstract = "We propose the use of parametric bootstrap methods to investigate the finitesample 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.",

keywords = "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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N2 - We propose the use of parametric bootstrap methods to investigate the finitesample 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.

AB - We propose the use of parametric bootstrap methods to investigate the finitesample 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.

KW - Small population

KW - age effect

KW - period effect

KW - cohort effect

KW - boot- strap

KW - parameter uncertainty

KW - systematic parameter difference

KW - likelihood ratio test

KW - power of test

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DO - 10.1007/s13385-016-0143-x

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SN - 2190-9733

VL - 7

SP - 193

EP - 230

JO - European Actuarial Journal

JF - European Actuarial Journal

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ER -

Small Population Bias and Sampling Effects in Stochastic Mortality Modelling

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Keywords

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Andrew John George Cairns

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