Measurement error is an important problem that has not been studied very well in the context of functional data analysis. To the best of our knowledge, there are no existing methods that address the presence of functional measurement errors in generalized functional linear models. In this article, a novel approach is proposed to estimate the slope function in the presence of measurement error in the generalized functional linear model with a scalar response. This work significantly advances the existing conditional score method to accommodate the case where both the measurement error and independent variables lie in infinite dimensional spaces. Asymptotic results are established for the proposed estimate, and its behaviour is studied via simulations, where the response is continuous or binary. Analysis of Canadian Weather data highlights the practical utility of our method. The Canadian Journal of Statistics 48: 238–258; 2020 © 2020 Statistical Society of Canada

中文翻译：

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功能回归中的功能测量误差

测量误差是一个重要的问题，尚未在功能数据分析的上下文中进行很好的研究。据我们所知，尚无解决通用功能线性模型中功能测量误差的方法。在本文中，提出了一种新颖的方法来估计具有标量响应的广义函数线性模型中存在测量误差的斜率函数。这项工作大大改进了现有的条件评分方法，以适应测量误差和自变量都位于无限维空间中的情况。为所提出的估计建立渐近结果，并通过仿真研究其行为，其中响应是连续的或二进制的。加拿大统计杂志48：238–258；加拿大 2020©2020加拿大统计学会