Extrapolation Estimation for Nonparametric Regression with Measurement Error

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