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Universal optimality of digital nets and lattice designs

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Abstract

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.

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Authors and Affiliations

  1. Laboratory of Mathematics and Applied Mathematics, School of Mathematical Sciences, Peking University, Beijing, 100871, China

    MingYao Ai

  2. Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL, 60616-3793, USA

    Fred J Hickernell

Authors
  1. MingYao Ai
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  2. Fred J Hickernell
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Corresponding author

Correspondence to MingYao Ai.

Additional information

This work was 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), and US National Science Foundation (Grant No. NSF-DMS-0713848)

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Ai, M., Hickernell, F.J. Universal optimality of digital nets and lattice designs. Sci. China Ser. A-Math. 52, 2309–2320 (2009). https://doi.org/10.1007/s11425-009-0171-y

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  • DOI: https://doi.org/10.1007/s11425-009-0171-y

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