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TEST OF SIGNIFICANCE FOR HIGH-DIMENSIONAL LONGITUDINAL DATA.

Ethan X Fang1, Yang Ning2, Runze Li1

  • 1Department of Statistics, the Pennsylvania State University, University Park, PA 16802-2111, USA.

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This study introduces a novel statistical method for analyzing longitudinal data with many covariates. The approach effectively constructs confidence intervals and controls the false discovery rate (FDR) in ultrahigh dimensions.

Keywords:
False discovery rategeneralized estimating equationquadratic inference function

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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.