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Targeted Inference Involving High-Dimensional Data Using Nuisance Penalized Regression.

Qiang Sun1, Heping Zhang2

  • 1Department of Statistical Sciences, University of Toronto, Toronto, Ontario M5S 3G3, Canada.

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|September 20, 2021
PubMed
Summary
This summary is machine-generated.

This study introduces nuisance penalized regression for analyzing high-dimensional data. The method effectively estimates parameters of interest, even when correlated with nuisance variables, simplifying statistical inference.

Keywords:
Efficient InferenceParameter of InterestParameter of NuisanceProfile LikelihoodSelective InferenceSparsity

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Area of Science:

  • Statistics
  • Data Analysis

Background:

  • High-dimensional data analysis is increasingly important in statistics.
  • Often, analysis focuses on specific variables (interest parameters) while others are considered nuisance parameters.

Purpose of the Study:

  • To develop a novel regression method that distinguishes between interest and nuisance parameters.
  • To provide a robust statistical inference framework for high-dimensional data.

Main Methods:

  • Proposed nuisance penalized regression, which avoids penalizing parameters of interest.
  • Developed an iterative procedure and a modified profile likelihood statistic for cases with coherence between parameters.

Main Results:

  • The proposed estimator allows direct inference when interest and nuisance parameters are uncorrelated.
  • An iterative refinement and hypothesis testing statistic are effective when parameters are correlated.

Conclusions:

  • Nuisance penalized regression offers a flexible and effective approach for high-dimensional data analysis.
  • The method simplifies inference and is validated through examples and numerical studies.