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Simultaneous Inference for High-Dimensional Approximate Factor Model.

Yong Wang1, Xiao Guo2

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Summary
This summary is machine-generated.

This study introduces a new method for simultaneous inference on factor loadings in approximate factor models. The approach uses a multiplier bootstrap for accurate critical values, enhancing multiple testing control.

Keywords:
high-dimensional factor modelmultiple testingmultiplier bootstrapsimultaneous inference

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Area of Science:

  • Econometrics
  • Statistical Inference
  • Multivariate Analysis

Background:

  • Approximate factor models are widely used for dimensionality reduction.
  • Simultaneous inference for factor loadings presents statistical challenges.
  • Existing methods may lack robustness or computational efficiency.

Purpose of the Study:

  • To develop a novel statistical test for simultaneous inference on factor loadings.
  • To provide a computationally efficient method for determining critical values.
  • To apply the developed methodology to control the family-wise error rate in multiple testing scenarios.

Main Methods:

  • Proposing a test statistic based on the maximum discrepancy measure.
  • Developing a multiplier bootstrap procedure for critical value calculation.
  • Analyzing the asymptotic size and power properties of the proposed test.

Main Results:

  • The multiplier bootstrap procedure provides accurate critical values for the test statistic.
  • The proposed test demonstrates desirable asymptotic size and power properties.
  • The methodology effectively controls the family-wise error rate (FWER) in multiple testing.

Conclusions:

  • The developed simultaneous inference method is statistically sound and computationally feasible.
  • The approach offers a robust tool for analyzing factor loadings in econometrics.
  • Simulation studies and real data analysis confirm the practical utility and effectiveness of the proposed method.