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A0818
Title: U-processes of diverging dimensional parameters Authors:  Yuanyuan Lin - The Chinese University of Hong Kong (Hong Kong) [presenting]
Zhanfeng Wang - University of Science and Technology of China (China)
Wenxin Liu - The Chinese University of Hong Kong (Hong Kong)
Qi-Man Shao - The Chinese University of Hong Kong (Hong Kong)
Abstract: A general theory for estimation methods based on U-process typed objective functions with parameter of increasing dimensions is derived. Under reasonable conditions, we establish a maximal inequality for degenerate U-processes with increasing dimensional parameter, and prove the sqrt(n/p)-consistency and asymptotic normality of each component of the resultant estimator of their linear combinations. Moreover, with increasing dimensionality, a general theory for random weighting resampling for U-process typed objective function is proposed and justified rigorously for inference. The theory is illustrated with the Han's maximum rank correlation estimation and the Gehan's estimation. Particularly, when the dimension of the parameter space diverges at the order of $o(\sqrt{n}/\log(n))$, the Han's maximum rank correlation estimator and the Gehan's estimator are shown to be $\sqrt{n/p}$-consistent, and their component-wise asymptotic normality remains valid.