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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]

Abstract: In this paper, the concepts of clear effects, alias sets and grid representations are generalized to nonregular two-level designs. Many good generalized join designs of n runs with resolution IV or more containing many clear two-factor interactions are given for up to 192 and n being a multiple of 16. The designs constructed are shown to have concise generalized two-factor interaction grid representations. Finally, theoretical results for the necessary and sufficient conditions under which there exist nonregular two-level designs of resolution IV or more containing clear two-factor interactions are proved. [Copyright &y& Elsevier]