  For the nonparametric regression models with covariates contaminated with
normal measurement errors, this paper proposes an extrapolation algorithm to
estimate the nonparametric regression functions. By applying the conditional
expectation directly to the kernel-weighted least squares of the deviations
between the local linear approximation and the observed responses, the proposed
algorithm successfully bypasses the simulation step needed in the classical
simulation extrapolation method, thus significantly reducing the computational
time. It is noted that the proposed method also provides an exact form of the
extrapolation function, but the extrapolation estimate generally cannot be
obtained by simply setting the extrapolation variable to negative one in the
fitted extrapolation function if the bandwidth is less than the standard
deviation of the measurement error. Large sample properties of the proposed
estimation procedure are discussed, as well as simulation studies and a real
data example being conducted to illustrate its applications.
