Extrapolation estimation for nonparametric regression with measurement error

• Published in: Scandinavian journal of statistics Vol. 51; no. 1; pp. 1 - 31
• Main Authors: Song, Weixing, Ayub, Kanwal, Shi, Jianhong
• Format: Journal Article
• Language: English
• Published: Oxford Blackwell Publishing Ltd 01.03.2024
• Subjects: Algorithms; Computing time; Error analysis; Extrapolation; local linear smoothing; measurement error; nonparametric regression; Regression models; Simulation; simulation and extrapolation
• ISSN: 0303-6898; 1467-9469
• DOI: 10.1111/sjos.12670

For the nonparametric regression models with covariates contaminated with the normal measurement errors, this paper proposes an extrapolation algorithm to estimate the 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 in the classical simulation extrapolation, thus significantly reducing the computational time. It is noted that the proposed method also provides an exact form of the extrapolation function, although 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 SD 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.