Kernel Regression Estimators for Nonparametric Model Calibration in Survey Sampling

Abstract

This paper introduces new kernel regression estimators with strictly non-negative smoothing weights that are iteratively adjusted. One estimator shares the “optimal” asymptotic bias and variance of the local linear regressor. Other estimators have zero sum of residuals, a desirable property in many applications. In a survey sampling context these estimators can easily be adjusted so that they are internally bias calibrated, which is a property with intuitive appeal. We demonstrate in simulations that one of the estimators with zero sum residuals has bias and variance properties that are very close to “optimal”. In addition, we propose a potentially useful refinement to the usual orders of asymptotic approximations for bias and variance of kernel regression smoothers. The smoothers are illustrated using two examples from fisheries applications, one of which involves data from a stratified random bottom-trawl survey.

Key Words:

• Kernel smoothing
• Residuals
• Nonparametric regression
• Nadaraya-Watson estimator
• Mack-Müller estimator
• Local linear estimator