Model-calibrated k-nearest neighbor estimators

Abstract

A generalized difference, a model-calibrated (MC), and a pseudo-empirical likelihood (PEMLE) kNN estimator of a population mean and its sampling variance was assessed with simulated simple random (SRS) and one-stage cluster sampling (CLU) from three artificial and one actual multivariate populations. The number of nearest neighbors (k) for imputing values of a target variable varied from one to eight. The design-based MC estimator had the lowest bias, but bias varied among populations and target variables. In terms of root mean squared errors (RMSEs), the estimators had similar performance, yet RMSEs of MC and PEMLE were less variable. Results were uneven across populations and target variables. The value of k had little effect on RMSE suggesting an advantage of choosing a low value that retains most of the attribute variance in a map. Nominal confidence intervals computed from MC estimators of variance achieved overall the best coverage rate. Rankings of the estimators in SRS and CLU designs were similar. We recommend MC for practical kNN applications in forest inventories for pixel-level predictions and derived estimates.