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Inference for sparse linear regression based on the leave-one-covariate-out solution path.

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  • 1216 LeConte College, 1523 Greene St, Columbia, SC 29201, USA.

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Summary
This summary is machine-generated.

We introduce a new method to assess variable importance in high-dimensional regression using the Least Absolute Shrinkage and Selection Operator (LASSO) solution path. This approach enhances variable screening and hypothesis testing for accurate statistical inference.

Keywords:
bootstraphigh-dimensional inferenceregressionvariable selection

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Area of Science:

  • Statistics
  • Machine Learning
  • Econometrics

Background:

  • High-dimensional data presents challenges for traditional statistical inference.
  • Variable importance and selection are critical in regression analysis.
  • Existing methods for high-dimensional inference have limitations.

Purpose of the Study:

  • To propose a novel measure of variable importance in high-dimensional regression.
  • To develop a new procedure for variable screening and hypothesis testing.
  • To extend the proposed method to logistic regression models.

Main Methods:

  • Leave-one-covariate-out analysis of the LASSO solution path.
  • Bootstrap techniques for constructing null distributions.
  • Application to both linear and logistic regression models.

Main Results:

  • The proposed method provides a novel way to calculate variable importance and screen variables.
  • Accurate p-values can be constructed for testing individual coefficients and multiple hypotheses.
  • The method demonstrates higher power than the t-test in low dimensions and outperforms other high-dimensional methods.

Conclusions:

  • The leave-one-covariate-out solution path approach is effective for variable importance and inference in high-dimensional regression.
  • The method provides accurate p-values and demonstrates superior power compared to existing techniques.
  • The approach is adaptable to logistic regression, offering a versatile tool for statistical analysis.