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Multiple robustness in factorized likelihood models.

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Summary
This summary is machine-generated.

This study introduces multiply robust estimating functions for nonparametric and semiparametric models. These functions ensure accurate parameter estimation even when auxiliary models for nuisance functions are misspecified.

Keywords:
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Area of Science:

  • Statistics
  • Statistical Inference
  • Nonparametric Statistics
  • Semiparametric Models

Background:

  • In statistical inference, estimating parameters often requires handling nuisance functions.
  • Existing methods can be sensitive to the correct specification of models for these nuisance functions.

Purpose of the Study:

  • To develop novel estimating functions that are robust to misspecification of nuisance function models.
  • To explore structures that facilitate the construction of multiply robust estimating functions.

Main Methods:

  • Considered nonparametric and semiparametric models with factorized likelihoods.
  • Investigated finite-dimensional parameters dependent on single likelihood factors.
  • Developed multiply robust estimating functions requiring multiple dimension-reducing models.

Main Results:

  • Multiply robust estimating functions were constructed.
  • These functions maintain a mean of zero at the true parameter value if at least one postulated auxiliary model is correct.
  • Demonstrated robustness against misspecification of nuisance function models.

Conclusions:

  • The proposed multiply robust estimating functions offer a flexible and robust approach to statistical inference.
  • This methodology enhances parameter estimation accuracy in complex statistical models.
  • Provides a framework for improved handling of nuisance parameters in various statistical applications.