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Abstract: The ``curse of dimensionality- has remained a challenge for high-dimensionaldata analysis in statistics. The sliced inverse regression SIR and canonicalcorrelation CANCOR methods aim to reduce the dimensionality of data byreplacing the explanatory variables with a small number of composite directionswithout losing much information. However, the estimated composite directionsgenerally involve all of the variables, making their interpretation difficult.To simplify the direction estimates, Ni, Cook and Tsai Biometrika 92 2005242-247 proposed the shrinkage sliced inverse regression SSIR based on SIR.In this paper, we propose the constrained canonical correlation $C^3$ methodbased on CANCOR, followed by a simple variable filtering method. As a result,each composite direction consists of a subset of the variables forinterpretability as well as predictive power. The proposed method aims toidentify simple structures without sacrificing the desirable properties of theunconstrained CANCOR estimates. The simulation studies demonstrate theperformance advantage of the proposed $C^3$ method over the SSIR method. Wealso use the proposed method in two examples for illustration.



Author: Jianhui Zhou, Xuming He

Source: https://arxiv.org/







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