TEST OF SIGNIFICANCE FOR HIGH-DIMENSIONAL LONGITUDINAL DATA

Area of Science:

• Statistics
• Biostatistics
• Econometrics

Background:

• Longitudinal data analysis presents challenges with ultrahigh-dimensional covariates and complex within-subject correlations.
• Constructing powerful statistical inference procedures in the presence of high-dimensional nuisance parameters is a significant hurdle.

Purpose of the Study:

• To develop robust statistical inference methods for longitudinal data with ultrahigh-dimensional covariates.
• To construct accurate confidence intervals and hypothesis tests for low-dimensional parameters of interest.
• To control the false discovery rate (FDR) in high-dimensional regression settings for longitudinal data.

Main Methods:

• Proposal of a quadratic decorrelated inference function approach to handle nuisance parameters and within-subject correlation.
• Theoretical analysis proving asymptotic normality and semiparametric efficiency for fixed-dimensional parameters of interest.
• Extension to scenarios where the parameter dimension grows polynomially with sample size.
• Application of Storey's procedure for FDR control in high-dimensional regression.

Main Results:

• The proposed method achieves asymptotic normality and attains the semiparametric information bound for fixed-dimensional parameters.
• An optimal Wald test statistic is constructed based on the derived asymptotic properties.
• The procedure effectively controls the false discovery rate (FDR) asymptotically in longitudinal data settings.
• Simulation studies confirm the procedure's ability to control Type I error and FDR in finite samples.

Conclusions:

• The novel quadratic decorrelated inference function approach provides a powerful and efficient tool for statistical inference in ultrahigh-dimensional longitudinal data.
• The developed methods offer reliable control of Type I errors and FDR, demonstrating practical utility in both theoretical and real-world applications.