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    Area of Science:

    • Statistics
    • High-dimensional data analysis
    • Statistical modeling

    Background:

    • High-dimensional linear models present challenges in variable significance testing due to high correlations.
    • Identifiability issues necessitate focusing on groups of variables rather than individual ones.
    • Existing methods may lack power or struggle with complex variable structures.

    Purpose of the Study:

    • To develop a general, modular method for significance testing of variable groups in high-dimensional linear models.
    • To address challenges posed by high correlations among covariables.
    • To provide a statistically robust approach with improved power and error rate control.

    Main Methods:

    • The proposed method utilizes repeated sample splitting and sequential rejection.
    • It allows for the incorporation of hierarchical structures within variable clusters.
    • The approach is designed to be modular and applicable to any set of variable clusters.

    Main Results:

    • The method asymptotically controls the familywise error rate.
    • It demonstrates improved statistical power compared to standard non-sequential rejection methods.
    • Empirical results from simulated and real data support the theoretical findings.

    Conclusions:

    • The developed method offers a powerful and reliable approach for group significance testing in high-dimensional settings.
    • It effectively handles highly correlated variables by focusing on group-level inference.
    • The modularity and hierarchical capabilities make it a versatile tool for various statistical analyses.