标题： 解析扰动与统计建模和推断中的系统偏差 显示英文标题

标题： Analytic perturbations and systematic bias in statistical modeling and inference

摘要： 在本文中，我们对线性及相关模型中的统计推断进行了全面研究，这些模型在其设计矩阵和协方差矩阵中表现出一些解析扰动。 我们还指出了几个潜在的应用。 在线性算子的扰动理论中，长期以来人们已经知道所谓的“奇异扰动”即使其大小很小，也可能对涉及这些算子的方程的解产生重大影响。 似乎到目前为止，关于这种不利现象是否也会出现在统计模型及其解中，还没有被正式研究过。 本文考虑的模型出现在非线性模型的背景下，其中只有一个参数用于描述非线性。 显示英文摘要

摘要： In this paper we provide a comprehensive study of statistical inference in linear and allied models which exhibit some analytic perturbations in their design and covariance matrices. We also indicate a few potential applications. In the theory of perturbations of linear operators it has been known for a long time that the so-called ``singular perturbations'' can have a big impact on solutions of equations involving these operators even when their size is small. It appears that so far the question of whether such undesirable phenomena can also occur in statistical models and their solutions has not been formally studied. The models considered in this article arise in the context of nonlinear models where a single parameter accounts for the nonlinearity.