Universal optimality of digital nets and lattice designs. (English) Zbl 1178.62080
Summary: 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, necessary and sufficient conditions for lattice designs being \(\varphi _{p }\)- 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.
MSC:
| 62K05 | Optimal statistical designs |
| 62K15 | Factorial statistical designs |
| 62G08 | Nonparametric regression and quantile regression |
| 62K10 | Statistical block designs |
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