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A test of homogeneity for age-dependent branching processes with immigration

机译：随年龄变化的分支过程的同质性检验

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摘要

We propose a novel procedure to test whether the immigration process of a discretely observed age-dependent branching process with immigration is time-homogeneous. The construction of the test is motivated by the behavior of the coefficient of variation of the population size. When immigration is time-homogeneous, we find that this coefficient converges to a constant, whereas when immigration is time-inhomogeneous it is time-dependent, at least transiently. Thus, we test the assumption that the immigration process is time-homogeneous by verifying that the sample coefficient of variation does not vary significantly over time. The test is simple to run and does not require specification or fitting any branching process to the data. Its implementation is identical whether the process is sub-, super-, or critical. Simulations and an application to real data on the progression of leukemia are presented to illustrate the approach.
机译：我们提出了一种新颖的程序来测试离散观察的与年龄相关的分支过程随时间的迁移过程是否时间均匀。该测试的构建是受总体大小变异系数的影响。当移民是时间均质的时，我们发现该系数收敛于一个常数，而当移民是时间非均质的时，它是时间相关的，至少是瞬时的。因此，我们通过验证样本变异系数不会随时间显着变化来测试移民过程是时间均匀的假设。该测试易于运行，不需要规格说明或对数据进行任何分支处理。无论过程是子过程，超级过程还是关键过程，其实现都是相同的。本文介绍了模拟方法以及对白血病进展的真实数据的应用，以说明该方法。

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