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Instrument Assisted Regression for Errors in Variables Models with Binary Response.

Kun Xu1, Yanyuan Ma1, Liqun Wang2

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Summary
This summary is machine-generated.

This study addresses errors-in-variables problems in binary response models using instrumental variables. A new consistent estimator is developed, offering a robust solution for complex statistical modeling.

Keywords:
binary responseconditional scoresconsistencyerrors in variablesgeneralized linear modelsinstrumental variableslogistic regressionmeasurement errorsemiparametric efficiency

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Area of Science:

  • Statistics
  • Econometrics
  • Biostatistics

Background:

  • Errors-in-variables (EIV) models are common in statistical analysis.
  • Binary response models are frequently used in various fields.
  • Instrumental variables (IV) offer a potential solution for EIV problems.

Purpose of the Study:

  • To develop a consistent estimator for binary response models with errors-in-variables.
  • To leverage instrumental variables for improved estimation accuracy.
  • To provide a method applicable to generalized linear models and beyond.

Main Methods:

  • Utilizing the prediction relationship between unobservable variables and instrumental variables.
  • Constructing a novel consistent estimator.
  • Establishing asymptotic properties of the proposed estimator.
  • Conducting simulation studies to validate the estimator.

Main Results:

  • The proposed estimator demonstrates consistency.
  • Simulation studies confirm the estimator's performance.
  • The method is shown to be generalizable to other models.

Conclusions:

  • The developed method provides a reliable approach for handling errors-in-variables in binary response settings.
  • The technique is adaptable to a broader range of generalized linear models.
  • The approach is validated through simulations and a real-world data example.