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首页> 外文期刊>Australian & New Zealand journal of statistics >A STATISTICAL TEST OF CHANGE-POINT IN MEAN THAT ALMOST SURELY HAS ZERO ERROR PROBABILITIES
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A STATISTICAL TEST OF CHANGE-POINT IN MEAN THAT ALMOST SURELY HAS ZERO ERROR PROBABILITIES

机译：几乎肯定具有零误差概率的均值变化统计检验

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摘要

In this paper we develop a non-conventional statistical test for the change-point in a mean model by making use of an almost-sure (a.s.) convergence (or strong convergence) result that we obtain, in respect of the difference between the sums of squared residuals under the null and alternative hypotheses. We prove that both types of error probabilities of the new test converge to zero almost surely when the sample size goes to infinity. This result does not hold for any conventional statistical test where the type I error probability, i.e. the significance level or the size, is prescribed at a low but non-zero level (e.g. 0.05). The test developed is easy to use in practice, and is ready to be generalised to other change-point models provided that the relevant almost-sure convergence results are available. We also provide a simulation study in the paper to compare the new and conventional tests under different data scenarios. The results obtained are consistent with our asymptotic study. In addition we provide least squares estimators of those parameters used in the change-point test together with their almost-sure convergence properties.
机译：在本文中，我们利用求和结果之间的几乎确定的（作为）收敛（或强收敛）结果，对均值模型中的变化点进行了非常规的统计检验。原假设和替代假设下的残差平方。我们证明，当样本量达到无穷大时，新测试的两种错误概率几乎可以肯定地收敛为零。对于任何将I型错误概率（即显着性水平或大小）规定为较低但非零的水平（例如0.05）的常规统计检验，该结果均不成立。所开发的测试易于在实践中使用，并且只要相关的几乎确定的收敛结果可用，就可以将其推广到其他变更点模型。我们还在本文中提供了一个仿真研究，以比较不同数据场景下的新测试和常规测试。获得的结果与我们的渐近研究一致。此外，我们提供了在变更点测试中使用的那些参数的最小二乘估计量，以及它们几乎确定的收敛特性。

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