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Statistical Inference for High-Dimensional Models via Recursive Online-Score Estimation.

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Summary
This summary is machine-generated.

This study introduces a novel method for estimating regression coefficients in high-dimensional generalized linear models. The new confidence interval (CI) offers valid coverage and is asymptotically narrower than existing methods.

Keywords:
Confidence intervalGeneralized linear modelsOnline estimationUltrahigh dimensions

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Area of Science:

  • Statistics
  • Econometrics
  • Machine Learning

Background:

  • High-dimensional generalized linear models (GLMs) present challenges in estimating regression coefficients.
  • Existing methods often struggle with a large number of predictors relative to sample size.

Purpose of the Study:

  • To develop a new estimation and valid inference method for regression coefficients in high-dimensional GLMs.
  • To construct a confidence interval (CI) with valid coverage and improved asymptotic properties.

Main Methods:

  • A novel estimator computed by solving a score function.
  • Recursive model selection to reduce dimensionality.
  • Construction of a score equation based on selected variables.

Main Results:

  • The proposed confidence interval (CI) achieves valid coverage without assuming model selection consistency.
  • Asymptotic CI length matches the oracle method when selection consistency is achieved.
  • The proposed CI is asymptotically narrower than de-sparsified Lasso and decorrelated score statistics.

Conclusions:

  • The developed method provides a statistically sound and efficient approach for inference in high-dimensional GLMs.
  • The proposed CI offers advantages in terms of coverage validity and asymptotic efficiency.
  • Empirical validation through simulations and real data applications supports the theoretical findings.