Unbiased Quasi-regression*

Abstract

Quasi-regression, motivated by the problems arising in the computer experiments, focuses mainly on speeding up evaluation. However, its theoretical properties are unexplored systemically. This paper shows that quasi-regression is unbiased, strong convergent and asymptotic normal for parameter estimations but it is biased for the fitting of curve. Furthermore, a new method called unbiased quasi-regression is proposed. In addition to retaining the above asymptotic behaviors of parameter estimations, unbiased quasi-regression is unbiased for the fitting of curve.

Keywords

Computer experiment / Quasi-regression / Unbiasedness / Fitting of curve / Asymptotic normality / 62G20 / 62J05

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