An increasingly popular tool for nonparametric smoothing are penalized splines (P-splines) which use low-rank spline bases to make computations tractable while maintaining accuracy as good as smoothing splines. This paper extends penalized spline methodology by both modeling the variance...

The paper introduces a new local polynomial estimator and develops supporting asymptotic theory for nonparametric regression in the presence of covariate measurement error. We address the measurement error with Cook and Stefanski's simulation-extrapolation (SIMEX) algorithm. Our method improves...