Generalized Quasi-Regression

Abstract

Quasi-regression, an approach for approximating an unknown function on the unit cube in very high dimensions, has very high computational efficiency. In this article, generalized quasi-regression is introduced. Some theoretical results on the generalized quasi-regression are provided, and numerical examples are illustrated.

Keywords:

• Basis function
• Computer experiment
• Fitting function
• Quasi-regression

Mathematics Subject Classification:

• Primary 62G20
• Secondary 62J05

Acknowledgments

The author would like to thank the editor, the associate editor, and the referees for their valuable comments which have led to a substantial improvement in this article. The research is partially supported by the Philosophy and Social Science Foundation of China (No. 07CTJ002) and the China Postdoctoral Science Foundation (No. 20060390169), the NNSF of China (No. 10671099).