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Abstract: Quasi-regression and generalized quasi-regression have been used as an approximation to an unknown function on the unit cube of very high dimensions. However, the fitting functions constructed by the two methods in the literature have biases. A new method called unbiased generalized quasi-regression is introduced. Theoretical results show that the new estimators of scalar coefficients and the fitting function have unbiasedness at the same time. Several numerical examples demonstrate that the unbiased generalized quasi-regression often has smaller residual errors than quasi-regression and generalized quasi-regression. [Copyright &y& Elsevier]