A new reproducing kernel‐based nonlinear dimension reduction method for survival data

Author:

Cui Wenquan1ORCID,Xu Jianjun1,Wu Yuehua2

Affiliation:

1. International Institute of Finance, School of Management University of Science and Technology of China Hefei China

2. Department of Mathematics and Statistics York University Toronto Ontario Canada

Abstract

AbstractBased on the theories of sliced inverse regression (SIR) and reproducing kernel Hilbert space (RKHS), a new approach RDSIR (RKHS‐based Double SIR) to nonlinear dimension reduction for survival data is proposed. An isometric isomorphism is constructed based on the RKHS property, then the nonlinear function in the RKHS can be represented by the inner product of two elements that reside in the isomorphic feature space. Due to the censorship of survival data, double slicing is used to estimate the weight function to adjust for the censoring bias. The nonlinear sufficient dimension reduction (SDR) subspace is estimated by a generalized eigen‐decomposition problem. The asymptotic property of the estimator is established based on the perturbation theory. Finally, the performance of RDSIR is illustrated on simulated and real data. The numerical results show that RDSIR is comparable with the linear SDR method. Most importantly, RDSIR can also effectively extract nonlinearity from survival data.

Funder

National Natural Science Foundation of China

Natural Sciences and Engineering Research Council of Canada

Publisher

Wiley

Subject

Statistics, Probability and Uncertainty,Statistics and Probability

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