摘要
This article considers universal optimality of digital nets and lattice designs in a regression model. Based on the equivalence theorem for matrix means and majorization theory,the necessary and sufficient conditions for lattice designs being φp-and universally optimal in trigonometric function and Chebyshev polynomial regression models are obtained. It is shown that digital nets are universally optimal for both complete and incomplete Walsh function regression models under some specified conditions,and are also universally optimal for complete Haar wavelet regression models but may not for incomplete Haar wavelet regression models.
This article considers universal optimality of digital nets and lattice designs in a regression model. Based on the equivalence theorem for matrix means and majorization theory, the necessary and sufficient conditions for lattice designs being φ p - and universally optimal in trigonometric function and Chebyshev polynomial regression models are obtained. It is shown that digital nets are universally optimal for both complete and incomplete Walsh function regression models under some specified conditions, and are also universally optimal for complete Haar wavelet regression models but may not for incomplete Haar wavelet regression models.
基金
supported by National Natural Science Foundation of China (Grant No. 10671007)
National Basic Research Program of China (Grant No. 2007CB512605)
Hong Kong Research Grants Council (Grant No. RGC/HKBU/2030/99P)
Hong Kong Baptist University (Grant No. FRG/00-01/II-62)
US National Science Foundation (Grant No. NSF-DMS-0713848)
