AI 中文总结
针对协变量含经典与Berkson混合测量误差的多项式回归模型，采用Corrected Score方法构造一致估计量，推导其渐近正态性条件并通过模拟验证结果。
AI 中文摘要
本文研究多项式结构回归模型，其中协变量观测时存在经典测量误差与Berkson测量误差的混合，经典误差、Berkson误差的方差及部分高阶矩均假设为已知。在无正态性假设的条件下，采用Corrected Score方法构造模型参数的一致估计量，并给出其渐近正态性的条件；在温和条件下，发现了渐近独立的估计量对，通过模拟研究验证了所得结果。
英文摘要
A polynomial structural regression model is studied, where the covariate is observed with a mixture of the classical and Berkson measurement errors. Both variances of the classical and Berkson errors, as well as some of their higher moments are assumed to be known. Without normality assumptions, consistent estimators of model parameters are constructed using the Corrected Score method, and conditions for their asymptotic normality are given. Under mild conditions, we found pairs of asymptotically independent estimators. A simulation study illustrates the results.
Comments18 pages, 7 figures
