An inference procedure is proposed to provide consistent estimators of parameters in a modal regression model with a covariate prone to measurement error. A score-based diagnostic tool exploiting parametric bootstrap is developed to assess adequacy of parametric assumptions imposed on the regression model. The proposed estimation method and diagnostic tool are applied to synthetic data generated from simulation experiments and data from real-world applications to demonstrate their implementation and performance. These empirical examples illustrate the importance of adequately accounting for measurement error in the error-prone covariate when inferring the association between a response and covariates based on a modal regression model that is especially suitable for skewed and heavy-tailed response data.

翻译：本文提出了一种推断方法，用于为存在测量误差的协变量众数回归模型提供参数的一致估计量。通过开发一种基于参数化自助法的评分诊断工具，评估回归模型参数假设的充分性。所提出的估计方法和诊断工具应用于仿真实验生成的合成数据及实际应用数据，以展示其实现过程与性能。这些实证案例表明，在基于特别适用于偏态和厚尾响应数据的众数回归模型推断响应变量与协变量之间的关联时，充分考量含误差协变量的测量误差至关重要。