Kernel Regression Utilizing External Information as Constraints
Chi-Shian Dai, Jun Shao · Statistica Sinica · 2022
With advanced technologies in data collection and storage, data analysis in modern scientific research and practice has shifted from analyzing a single dataset to coupling several datasets.Article Chatterjee et al. (2016) proposes a parametric likelihood approach for analyzing a main "internal" dataset using constraints formulated with information from an additional "external" dataset.In this article, we consider nonparametric kernel regression in an internal dataset analysis utilizing constraints for auxiliary information from an external dataset with summary statistics.Under some conditions, we show that the proposed constrained kernel regression estimator is asymptotically normal and is better than the standard kernel regression without using external information in terms of the asymptotic mean integrated square error.Furthermore, we consider the situation where internal and external data have different populations.Simulation results are obtained to confirm our theory and to quantify the improvements from utilizing external data.An example of application is also included for illustration.