Summary Diagonal discriminant rules have been successfully used for high-dimensional classification problems, but suffer from the serious drawback of biased discriminant scores. In this paper, we propose improved diagonal discriminant rules with bias-corrected discriminant scores for high-dimensional classification. We show that the proposed discriminant scores dominate the standard ones under the quadratic loss function. Analytical results on why the bias-corrected rules can potentially improve the predication accuracy are also provided. Finally, we demonstrate the improvement of the proposed rules over the original ones through extensive simulation studies and real case studies.

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The complex crustal structure of northeastern South China Sea and neighboring areas, especially the structure of the land-sea transition zone, has been a hot subject of the lithospheric structure research of South China Sea. In this paper we construct the density model along two profiles based on gravity data and constraints from Pn wave tomography and deep seismic sounding. The result of 2.5D density modeling supports the point of view that a high velocity layer exists in the lower crust of the area from Qiongyue Uplift to Luzon island arc; and the fitting result to the Taixinan Basin indicates that the crust in the southern depressed region should belong to the transitional type. Although the tectonic feature of the northeastern shelf of South China Sea is generally of volcanic type, the structures of profile AA' and BB' are different, which indicates the lateral variation and the complexity of crustal structure in the northeastern margin of South China Sea.

a b s t r a c tThe Jiashan-Lujiang, Yishu and Bohai segments have been the most tectonically active parts of the Tan-Lu fault system since the Mesozoic. Any analysis of faulting processes in the Tan-Lu system is highly dependent on the relationships among the three segments. Here we divide the Tan-Lu system into three styles of faulting; strike-slip faulting, regional extensional faulting and listric normal faulting on the basis of EMAP data, seismic profiles and geological evidence. We suggest that: (1) the strike-slip faults, which formed in the Late Jurassic, include mainly the Jiashan-Lujiang fault, the deep parts of the Chihe-Taihu Fault and the Guhe-Sanbing fault; these three faults have had the most dramatic effect on the JiashanLujiang segment. The strike-slip style of faulting produced a huge positive-flower structure that extends between the deep section of the Chihe-Taihu fault and the Guhe-Sanbing fault, and overlaps with the position of the Zhangbaling ductile shear zone; (2) the regional extensional style of faulting, whose characteristics are reflected best in the Yishu fault zone, is composed of the Changyi-Dadian, Anqiu-Quxian, Yishui-Yangtou and Tangwu-Gegou faults, all of which were active during the Early Cretaceous. These extension-dominated faults extend southwards to the Jiashan and Hefei Basins and die out in front of the Dabie Mountains; to the north, the faults penetrate the deeper parts of the Weibei depression where they controlled Cretaceous deposition in ''graben-horst-graben'' structures; (3) the listric normal faults, which were initiated in the Paleogene, generally occur around the Bohai Bay Basin, and include a series of NE-trending faults in the Weibei depression, such as the Tandong and Tanxi faults. These listric faults differ from the regional extensional faults in their localized occurrence and association with basin formation. Our study indicates that these three styles of faulting varied not only in timing and mechanical properties but developed at different levels at different locations, resulting in different tectonic relationships and the formation of different geologic features in the different segments of the Tan-Lu master system.