论文标题
在对称性的皮尔森（Pearson）的自动估计中与异常值进行对称的型测试：正态性的鲁棒测试
On Symmetrized Pearson's Type Test in Autoregression with Outliers: Robust Testing of Normality
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 $）型号。自动降低参数尚不清楚，以及Innoovations的分布和力矩。异常值的分布$π$是未知的，任意的，它们的强度为$γn^{ - 1/2} $，未知$γ$，$ n $是样本量。自动进度参数是由$ n^{1/2} $的任何估计器估算的 - 在$γ\ leqγ<\ infty $中均匀均匀。使用来自估计的自动进度的残差，我们构建了一种经验分布函数（E.D.F.），这是（无法访问）E.D.F.的对应物。自动估计创新。我们获得了此E.D.F.的随机扩展，这使我们能够构建Pearson卡方类型的对称测试，以构建创新分布的正态性。我们根据$γ= 0 $的$γ$在限制水平（作为$γ$和$π$的功能）方面建立了这些测试的定性鲁棒性。
We consider a stationary linear AR($p$) model with observations subject to gross errors (outliers). The autoregression parameters are unknown as well as the distribution and moments of innoovations. The distribution of outliers $Π$ is unknown and arbitrary, their intensity is $γn^{-1/2}$ with an unknown $γ$, $n$ is the sample size. The autoregression parameters are estimated by any estimator which is $n^{1/2}$-consistent uniformly in $γ\leq Γ<\infty$. 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., which enables us to construct the symmetrized test of Pearson's chi-square type for the normality of distribution of innovations. We establish qualitative robustness of these tests in terms of uniform equicontinuity of the limiting levels (as functions of $γ$ and $Π$) with respect to $γ$ in a neighborhood of $γ=0$.
