Kernel Averaging Estimators
Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review
|Journal / Publication||Journal of Business and Economic Statistics|
|Online published||30 Nov 2021|
|Publication status||Online published - 30 Nov 2021|
|Link to Scopus||https://www.scopus.com/record/display.uri?eid=2-s2.0-85122028935&origin=recordpage|
The issue of bandwidth selection is a fundamental model selection problem stemming from the uncertainty about the smoothness of the regression. In this article, we advocate a model averaging approach to circumvent the problem caused by this uncertainty. Our new approach involves averaging across a series of Nadaraya-Watson kernel estimators each under a different bandwidth, with weights for these different estimators chosen such that a least-squares cross-validation criterion is minimized. We prove that the resultant combined-kernel estimator achieves the smallest possible asymptotic aggregate squared error. The superiority of the new estimator over estimators based on widely accepted conventional bandwidth choices in finite samples is demonstrated in a simulation study and a real data example.
- Asymptotic optimality, Cross-validation, Kernel estimation, Model average, Nonparametric regression