This paper introduces a new local polynomial estimator and develops supporting asymptotic theory for non-parametric 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 on previous local polynomial estimators for this problem by (1) using a bandwidth selection procedu...

We begin with the following question: given a closed disc D ⋐ C and a complex-valued function F ∈ C(D), is the uniform algebra on D generated by z and F equal to C(D) ? When F ∈ C 1 (D), this question is complicated by the presence of points in the surface S := graph D (F) that have complex tangents. Such points are called CR singularities. Let p ∈ S be a CR singularity at which the order of co...