标题： 测试多项式模型在变量误差问题中的适用性 显示英文标题

标题： Testing the suitability of polynomial models in errors-in-variables problems

摘要： 用于响应曲线的低次多项式模型在实践中被广泛使用。它通常包含协变量的线性或二次函数。在本文中，我们提出了当协变量存在误差时，检验一般多项式模型拟合优度的方法。在那里，真实的协变量并未直接观测到，因此传统的Bootstrap检验方法不适用。我们开发了一种新方法，其中使用反卷积方法来估计零假设下协变量的分布，并采用“野生”或矩匹配的Bootstrap论证来估计实验误差的分布（不同于协变量误差的分布）。我们大部分注意力集中在协变量误差的分布已知的情况下，尽管我们也讨论了当协变量误差分布被估计时的估计和检验方法。我们不对实验误差的分布做出任何假设，并且特别地，我们与传统的变量误差问题的参数模型有显著的不同。 显示英文摘要

摘要： A low-degree polynomial model for a response curve is used commonly in practice. It generally incorporates a linear or quadratic function of the covariate. In this paper we suggest methods for testing the goodness of fit of a general polynomial model when there are errors in the covariates. There, the true covariates are not directly observed, and conventional bootstrap methods for testing are not applicable. We develop a new approach, in which deconvolution methods are used to estimate the distribution of the covariates under the null hypothesis, and a ``wild'' or moment-matching bootstrap argument is employed to estimate the distribution of the experimental errors (distinct from the distribution of the errors in covariates). Most of our attention is directed at the case where the distribution of the errors in covariates is known, although we also discuss methods for estimation and testing when the covariate error distribution is estimated. No assumptions are made about the distribution of experimental error, and, in particular, we depart substantially from conventional parametric models for errors-in-variables problems.