Kernel regression utilizing heterogeneous datasets

Abstract

Data analysis in modern scientific research and practice has shifted from analysing a single dataset to coupling several datasets. We propose and study a kernel regression method that can handle the challenge of heterogeneous populations. It greatly extends the constrained kernel regression [Dai, C.-S., & Shao, J. (2023). Kernel regression utilizing external information as constraints. Statistica Sinica, 33, in press] that requires a homogeneous population of different datasets. The asymptotic normality of proposed estimators is established under some conditions and simulation results are presented to confirm our theory and to quantify the improvements from datasets with heterogeneous populations.

Keywords:

• Conditional expectation
• constraints
• data coupling and integration
• external data
• heterogeneous populations
• kernel estimation

Acknowledgments

The authors would like to thank two anonymous referees for helpful comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Jun Shao's research was partially supported by the National Natural Science Foundation of China [Grant Number 11831008] and the U.S. National Science Foundation [Grant Number DMS-1914411].