Abstract:
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We consider modal regression in the presence of measurement error. Empirical evidence suggests that ignoring measurement error can result in inconsistence inference on regression coefficients. To account for measurement error, we adopt the Monte Carlo corrected score method (Novick and Stefanski, 2002) to numerically approximate an unbiased sore function based on which we estimate the regression parameters consistently. To relax the normality assumption on measurement error required for the validity of Monte Carlo corrected score, we propose a second method where we analytically construct a corrected score using the deconvoluting kernel (Stefanski and Caroll, 1990). We rigorously study the asymptotic properties of corrected score estimators resulting from the second method. Numerical evidence from simulation study and a real-life application to dietary data suggest that the two proposed methods yield estimators that substantially outperform the naive estimator.
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