论文标题
自动估计中创新的对称性测试
Testing of symmetry of innovations in autoregression
论文作者
论文摘要
我们考虑一个固定线性$ ar（P）$型号为零。创新的自动化参数以及分布函数（d.f.）$ g（x）$尚不清楚。我们考虑两种情况。在第一种情况下，观察结果是$ ar（p）$的固定解决方案中的样本。有趣且必不可少的问题是相对于零来测试$ g（x）$的对称性。如果对称性的假设有效，则可以构建$ ar（p）$参数的非参数估计量，例如，GM估计器，最小距离估计器等。首先，我们估计自动估计的未知参数并找到残差。基于它们，我们构建了一种经验性的D.F.，它是无法观察到的创新的经验D.F的对应物。我们的测试统计量是从这种残留经验D.F.中的欧米茄平方体类型的功能。它的渐近D.F.在假设和局部替代方案下。在第二种情况下，观察结果遭受总错误（离群值）。异常值的分布未知，它们的强度为$ O（n^{ - 1/2}）$，$ n $是样本量。我们再次测试了创新的对称性，但是通过构建皮尔逊的统计数据。它的渐近D.F.在假设和局部替代方案下。我们也建立了该测试的渐近鲁棒性。
We consider a stationary linear $AR(p)$ model with zero mean. The autoregression parameters as well as the distribution function (d.f.) $G(x)$ of innovations are unknown. We consider two situations. In the first situation the observations are a sample from a stationary solution of $AR(p)$. Interesting and essential problem is to test symmetry of $G(x)$ with respect to zero. If hypothesis of symmetry is valid then it is possible to construct nonparametric estimators of $AR(p)$ parameters, for example, GM-estimators, minimum distance estimators and others. First of all we estimate unknown parameters of autoregression and find residuals. Based on them we construct a kind of empirical d.f., which is a counterpart of empirical d.f of the unobservable innovations. Our test statistic is the functional of omega-square type from this residual empirical d.f. Its asymptotic d.f. under the hypothesis and the local alternatives are found. In the second situation the observations subject to gross errors (outliers). The distribution of outliers is unknown, their intensity is $O(n^{-1/2})$, $n$ is the sample size. We test the symmetry of innovations again but by constructing the Pearson's type statistic. Its asymptotic d.f. under the hypothesis and the local alternatives are found. We establish the asymptotic robustness of this test as well.
