TY - JOUR

T1 - Inference for the dimension of a regression relationship using pseudo-covariates

AU - Huang, Shih Hao

AU - Shedden, Kerby

AU - Chang, Hsin wen

N1 - Publisher Copyright:
© 2022 The International Biometric Society.

PY - 2023/9

Y1 - 2023/9

N2 - In data analysis using dimension reduction methods, the main goal is to summarize how the response is related to the covariates through a few 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 work, we propose an easily-applied approach to conduct inference for the dimension of the SDR subspace, based on augmentation of the covariate set with simulated pseudo-covariates. Applying the partitioning principal to the possible dimensions, we use rigorous sequential testing to select the dimensionality, by comparing the strength of the signal arising from the actual covariates to that appearing to arise from the pseudo-covariates. We show that under a “uniform direction” condition, our approach can be used in conjunction with several popular SDR methods, including sliced inverse regression. In these settings, the test statistic asymptotically follows a beta distribution and therefore is easily calibrated. Moreover, the family-wise type I error rate of our sequential testing is rigorously controlled. Simulation studies and an analysis of newborn anthropometric data demonstrate the robustness of the proposed approach, and indicate that the power is comparable to or greater than the alternatives.

AB - In data analysis using dimension reduction methods, the main goal is to summarize how the response is related to the covariates through a few 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 work, we propose an easily-applied approach to conduct inference for the dimension of the SDR subspace, based on augmentation of the covariate set with simulated pseudo-covariates. Applying the partitioning principal to the possible dimensions, we use rigorous sequential testing to select the dimensionality, by comparing the strength of the signal arising from the actual covariates to that appearing to arise from the pseudo-covariates. We show that under a “uniform direction” condition, our approach can be used in conjunction with several popular SDR methods, including sliced inverse regression. In these settings, the test statistic asymptotically follows a beta distribution and therefore is easily calibrated. Moreover, the family-wise type I error rate of our sequential testing is rigorously controlled. Simulation studies and an analysis of newborn anthropometric data demonstrate the robustness of the proposed approach, and indicate that the power is comparable to or greater than the alternatives.

KW - inference for dimension

KW - nonparametric regression

KW - sequential testing

KW - sufficient dimension reduction

KW - variable augmentation

UR - http://www.scopus.com/inward/record.url?scp=85145190297&partnerID=8YFLogxK

U2 - 10.1111/biom.13812

DO - 10.1111/biom.13812

M3 - 期刊論文

C2 - 36511353

AN - SCOPUS:85145190297

SN - 0006-341X

VL - 79

SP - 2394

EP - 2403

JO - Biometrics

JF - Biometrics

IS - 3

ER -