Abstract

Joint factor models are commonly adopted to relate unobservable factors with covariates.

Traditional approaches to joint models often assume linear relationships between latent factors and

covariates, require prior knowledge of the number of latent factors, and typically fail to address

heavy-tailedness or high-dimensional covariates. To overcome these challenges, we propose a general factor-covariate model and introduce a new variable selection procedure to broaden the scope of

application and to alleviate the curse of dimensionality. The procedure is unfolded in three steps:

robust estimation of factors via Huber regression, feature screening using an index of mean squared

deviation (MSD) of conditional quantile and false discovery rate (FDR) control based on derandomized quantile knockoffs. To facilitate implementation, we employ smoothing quantile regression and

apply a modified bootstrap-based eigenvalue method to determine the number of factors. Theoretical

justifications on the sure screening property as well as the control of FDR, per family error rate and k

family-wise error rate are provided. The superiority of our proposed procedure over existing methods

is demonstrated by numerical studies on simulated and real datasets.

Information

Preprint No.SS-2025-0167
Manuscript IDSS-2025-0167
Complete AuthorsHan Pan, Wei Xiong, Mingyao Ai
Corresponding AuthorsMingyao Ai
Emailsmyai@math.pku.edu.cn

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Acknowledgments

The authors would like to thank the editor, associate editor and referees for their insightful

comments and suggestions that have significantly improved the paper. The first two authors

was supported by the Funds for Central Universities in UIBE CXTD14-05. Ai’s work was

supported by NSFC grants 12131001 and W2412023, and LMEQF.

Supplementary Materials

The properties of the MSD index under Gaussian distribution, details on the MSD knockoffs

procedure, v-quantile knockoffs and estimation of the MSD index, figures for convolutiontype smoothed quantile loss, as well as all technical proofs, additional results from numerical

studies are provided in the online Supplementary Materials

Supplementary materials are available for download.