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On high-dimensional Poisson models with measurement error: Hypothesis testing for nonlinear nonconvex optimization.

Fei Jiang1, Yeqing Zhou2, Jianxuan Liu3

  • 1Department of Epidemiology and Biostatistics, The University of California, San Francisco.

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|August 21, 2023
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Summary
This summary is machine-generated.

We developed a new method for Poisson regression with noisy, high-dimensional data. This approach corrects bias, performs variable selection, and enables robust statistical testing for complex datasets.

Keywords:
00X00High dimension InferenceMeasurement ErrorNon-convex optimizationPoisson modelPrimary 00X00secondary 00X00

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Area of Science:

  • Statistics
  • Machine Learning
  • Biostatistics

Background:

  • Poisson regression is widely used for count data analysis.
  • High-dimensional data and covariate noise present significant challenges in statistical modeling.
  • Existing methods often struggle with bias and variable selection in these complex scenarios.

Purpose of the Study:

  • To develop a robust estimation and testing framework for Poisson regression with noisy, high-dimensional covariates.
  • To address the non-convexity introduced by bias correction and the complexity of high dimensions.
  • To enable accurate variable selection and hypothesis testing in such models.

Main Methods:

  • Minimizing a penalized non-convex target function to estimate regression parameters.
  • Deriving L1 and L2 convergence rates for the proposed estimator.
  • Establishing asymptotic normality for subsets of parameters, including those growing infinitely slow.
  • Developing Wald and score tests based on the derived asymptotic properties.

Main Results:

  • The proposed estimator achieves optimal convergence rates (L1 and L2).
  • Variable selection consistency is proven.
  • Asymptotic normality is established for parameter subsets, enabling flexible testing.
  • Simulations demonstrate strong finite sample performance of the developed tests.

Conclusions:

  • The novel method effectively handles noisy, high-dimensional covariates in Poisson regression.
  • The framework provides reliable estimation, variable selection, and hypothesis testing capabilities.
  • Successful application to Alzheimer's Disease Neuroimaging Initiative data highlights practical utility.