The issues caused by measurement errors have been recognized for almost 90 years, and research in this area has flourished since the 1980s. We review some of the classical methods in both density estimation and regression problems with measurement errors. In both problems, we consider when the original error-free model is parametric, nonparametric, and semiparametric, in combination with different error types. We also summarize and explain some new approaches, including recent developments and challenges in the high-dimensional setting.

中文翻译：

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测量误差建模的更新


由测量误差引起的问题已经被认识到近 90 年，自 1980 年代以来，该领域的研究蓬勃发展。我们回顾了密度估计和带有测量误差的回归问题中的一些经典方法。在这两个问题中，我们都会考虑原始无误差模型是参数模型、非参数模型和半参数模型以及不同误差类型的模型。我们还总结和解释了一些新方法，包括高维环境中的最新发展和挑战。