论文标题
关于对称性皮尔逊类型测试的力量，在自动估计中与异常值进行自动估计
On the Power of Symmetrized Pearson's Type Test under Local Alternatives in Autoregression with Outliers
论文作者
论文摘要
我们考虑使用具有总数错误（离群值）的观测值的固定线性AR（$ p $）型号。自动化参数尚不清楚，并且创新的分销函数$ g $。异常值的分布$π$是未知的，任意的，它们的强度为$γn^{ - 1/2} $，未知$γ$，$ n $是样本量。我们测试假设$ h_0 \ colon g = g_0 $，simmetric $ g_0 $。我们在本地替代方案下找到测试的功能$ h_ {1n}（ρ）\ colon g =（1-ρn^{ - 1/2}）g_0+ρn^{ - 1/2} h $。我们的测试是特殊对称的皮尔逊类型测试。也就是说，首先，我们估计自动估计参数，然后使用来自估计的自动估计的残差，我们构建了一种经验分布函数（E.D.F.），这是（不可访问的）E.D.F.的对应物。自动估计创新。我们获得了此E.D.F.的随机扩展并在$ h_ {1n}（ρ）$下进行对称的变体，这使我们能够以$ h_0 $构建和调查对Pearson类型的对称测试。我们在$γ= 0 $的社区中，就限制能力的均匀等准（作为$γ，ρ$和$π$的功能）建立了该测试的定性鲁棒性。
We consider a stationary linear AR($p$) model with observations subject to gross errors (outliers). The autoregression parameters are unknown as well as the distribution function $G$ of innovations. The distribution of outliers $Π$ is unknown and arbitrary, their intensity is $γn^{-1/2}$ with an unknown $γ$, $n$ is the sample size. We test the hypothesis $H_0\colon G=G_0$ with simmetric $G_0$. We find the power of the test under local alternatives $H_{1n}(ρ)\colon G=(1-ρn^{-1/2})G_0+ρn^{-1/2}H$. Our test is the special symmetrized Pearson's type test. Namely, first of all we estimate the autoregression parameters and then using the residuals from the estimated autoregression we construct a kind of empirical distribution function (e.d.f.), which is a counterpart of the (inaccessible) e.d.f. of the autoregression innovations. We obtain a stochastic expansion of this e.d.f. and its symmetrized variant under $H_{1n}(ρ)$ , which enables us to construct and investigate our symmetrized test of Pearson's type for $H_0$. We establish qualitative robustness of this test in terms of uniform equicontinuity of the limiting power (as functions of $γ,ρ$ and $Π$) with respect to $γ$ in a neighborhood of $γ=0$.
