B‐spline modal estimation under measurement error with deconvolution

Abstract We investigate a B‐spline‐based estimation procedure for a semiparametric varying coefficient (SPVC) modal regression with an error‐prone linear covariate, where the true covariate is unobserved but an ancillary variable is available. The method targets mode values to capture the “most likely” effects rather than mean effects. Varying coefficients are approximated via B‐splines, and a deconvolution kernel‐based objective function is used for estimation. We establish consistency and asymptotic properties of the estimators under ordinary‐ and super‐smooth error distributions and discuss bandwidth selection. For comparison, asymptotic results for SPVC modal estimators without measurement error are also derived. Efficient implementation relies on a modified fast Fourier transform and a mode expectation–maximization algorithm. Monte Carlo simulations and an empirical application demonstrate the finite‐sample performance and practical utility of the proposed method.