Dimension Estimation in Sufficient Dimension Reduction through Pseudo-Covariates

Project Details


In data analysis using dimension reduction methods, the main purpose is to summarize how the response is related to the covariates through a limited set of their linear combinations. One key issue is to determine the number of independent, relevant covariate combinations, which is the dimension of the sufficient dimension reduction (SDR) subspace. In this proposal, we will propose a broadly applicable approach to estimate the dimensionality of the SDR subspace, based on augmentation of the covariate set with simulated pseudo-covariates. The dimensionality is estimated using sequential testing, which compares the strength of the signal arising from the original covariates to that arising from the pseudo-covariates. We expect to show that under a weak uniform-direction condition, our test statistic follows a beta distribution asymptotically under the null hypothesis, and therefore is easily calibrated.
Effective start/end date1/08/2031/07/21


  • dimension estimation
  • dimension reduction
  • eigen-decomposition
  • inverse regression
  • variable augmentation
  • simulation-based inference


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