Becker N
Biometrics. 1977 Sep;33(3):515-22.
Certain estimators for the mean of the offspring distribution of a Galton-Watson process are considered. The asymptotic behaviour of each of these estimators is studied when the true underlying model is in fact a multitype branching process or a branching process with a random environment. It is revealed which of the estimators remain consistent indicators of whether or not the process is subcritical, under these alternative underlying models. It is then indicated how this "robustness" result might influence the choice of an estimator by considering the problem of estimating the level of immunity required in a community in order to prevent major epidemics. The application is illustrated with references to smallpox using data from an outbreak in São Paulo, Brazil.
考虑了高尔顿-沃森过程子代分布均值的某些估计量。当真实的基础模型实际上是多类型分支过程或具有随机环境的分支过程时，研究了这些估计量各自的渐近行为。揭示了在这些替代基础模型下，哪些估计量仍然是该过程是否为亚临界的一致指标。然后通过考虑估计社区预防重大疫情所需免疫水平的问题，指出了这一“稳健性”结果可能如何影响估计量的选择。以巴西圣保罗一次天花疫情的数据为例说明了该应用。
