We consider a stationary linear AR(p) model with contamination (gross errors in the observations). The autoregression parameters are unknown, as well as the distribution of innovations. Based on the residuals from the parameter estimates, an analog of the empirical distribution function is defined and a test of Pearson’s chi-square type is constructed for testing hypotheses on the distribution of innovations. We obtain the asymptotic power of this test under local alternatives and establish its qualitative robustness under the hypothesis and alternatives.

中文翻译：

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局部选择下皮尔逊检验在离群值自回归中的功效

我们考虑带有污染（观测值中的总误差）的固定线性AR（p）模型。自回归参数以及创新的分布都是未知的。基于参数估计值的残差，定义了经验分布函数的类似物，并构造了Pearson卡方检验，以检验创新分布的假设。我们在局部选择下获得了该检验的渐近能力，并在假设和选择下建立了其定性鲁棒性。