Testing Composite Hypotheses for Locally Stationary Processes
Testing Composite Hypotheses for Locally Stationary Processes
复制标题
测试局部平稳过程的复合假设
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
M. Taniguchi
中科院分区：
文献类型：
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作者：
K. Sakiyama;M. Taniguchi
对于Dahlhaus引入的一类局部平稳过程，本文讨论了复合假设的检验问题。首先，对于高斯似然比检验（GLR）、Wald检验（W）和拉格朗日乘子检验（LM），我们导出了复合假设下的参数形式的极限分布。结果表明，在该假设下，GLR、W和LM的分布均趋于χ2分布。我们还评估了他们的局部权力下的一系列局部替代品，并讨论了他们的渐近最优性。其结果可用于平稳性检验。文中给出了一些实例。他们通过仿真阐明了局部功率特性。另一方面，我们提供了一个非参数LAN定理。在此基础上，我们得到了非参数形式的零假设和备择假设下GLR的极限分布。最后给出了数值研究。
For a class of locally stationary processes introduced by Dahlhaus, this paper discusses the problem of testing composite hypotheses. First, for the Gaussian likelihood ratio test (GLR), Wald test (W) and Lagrange multiplier test (LM), we derive the limiting distribution under a composite hypothesis in parametric form. It is shown that the distribution of GLR, W and LM tends to a χ2 distribution under the hypothesis. We also evaluate their local powers under a sequence of local alternatives, and discuss their asymptotic optimality. The results can be applied to testing for stationarity. Some examples are given. They illuminate the local power property via simulation. On the other hand, we provide a nonparametric LAN theorem. Based on this result, we obtain the limiting distribution of the GLR under both null and alternative hypotheses described in nonparametric form. Finally, the numerical studies are given.