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Abstract:
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This work presents the framework of a smooth polynomial model, named Smooth Ridge (SR) model which provides a new direction in the realm of smooth interpolation for computer experiments.It is shown that Ridge regression and standard regression models are special cases of SR model. Moreover, the model bears inherent feature of smoothness along with efficient interpolation irrespective of the singularity problem of design matrix.The prime purpose of the model is to provide improved predictions for out-of-sample unknown points along with quantification of prediction errors. Theoretical results supported by simulation studies provide the evidence that SR model outperforms its contemporary Design and Analysis of Computer Experiments(DACE) model.The performance of proposed model is also evaluated for the case when kriging is not supported by the observed data in which case the SR model with trend only provides efficient predictions at unknown points with least mean square error compared to Sacks model. In addition, the proposed model is fit to COVID data for aerosol transmission, where it outperformed the contemporary models in terms of efficient prediction of the response.
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