  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.
