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随机死亡率建模中的小群体偏差和抽样效应。

Small population bias and sampling effects in stochastic mortality modelling.

作者信息

Chen Liang, Cairns Andrew J G, Kleinow Torsten

机构信息

Actuarial Research Centre, Department of Actuarial Mathematics and Statistics and the Maxwell Institute for Mathematical Sciences, School of Mathematical and Computer Sciences, Heriot-Watt University, EH14 4AS Edinburgh, UK.

出版信息

Eur Actuar J. 2017;7(1):193-230. doi: 10.1007/s13385-016-0143-x. Epub 2017 Jan 23.

DOI:10.1007/s13385-016-0143-x
PMID:29323361
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC5744643/
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.

摘要

我们建议使用参数自助法来研究随机死亡率模型参数向量的最大似然估计量的有限样本分布。特别强调基础人口规模对有限样本中最大似然估计量分布的影响，以及所得估计量的相依结构：即我们模型中年龄、时期和队列效应估计量之间的相依性。此外，我们研究似然比检验统计量的分布，在其中我们检验关于模型中真实参数的原假设。最后，我们将似然比检验应用于根据英格兰和威尔士女性以及苏格兰男性的观察死亡率估计的队列效应。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4430/5744643/7f503ca9a712/13385_2016_143_Fig16_HTML.jpg
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https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4430/5744643/62de49a3dcd4/13385_2016_143_Fig8_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4430/5744643/116253ed2e34/13385_2016_143_Fig9_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4430/5744643/4befdf518316/13385_2016_143_Fig10_HTML.jpg
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本文引用的文献

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Identification and forecasting in mortality models.死亡率模型中的识别与预测
ScientificWorldJournal. 2014;2014:347043. doi: 10.1155/2014/347043. Epub 2014 Jun 2.
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A Bayesian forecasting model: predicting U.S. male mortality.一种贝叶斯预测模型：预测美国男性死亡率。
Biostatistics. 2006 Oct;7(4):530-50. doi: 10.1093/biostatistics/kxj024. Epub 2006 Feb 16.
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