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Taylor quasi-likelihood for limited generalized linear models.

Guangbao Guo1

  • 1Department of Statistics, Shandong University of Technology, Zibo, People's Republic of China.

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Summary
This summary is machine-generated.

This study introduces Taylor quasi-likelihood for estimating generalized linear models with limited dependent variables, resolving a key challenge in statistical modeling. The novel method offers consistent and asymptotically normal estimators, proving effective in simulations.

Keywords:
62E2062J0562J12Generalized linear modelsTaylor expansionhigh dimensionlimited dependent variablequasi-likelihood

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Area of Science:

  • Statistics
  • Econometrics
  • Biostatistics

Background:

  • Generalized linear models (GLMs) are widely used across disciplines.
  • A significant challenge exists in quasi-likelihood estimation for GLMs with limited dependent variables.
  • Existing methods struggle to provide unified estimation for these models.

Purpose of the Study:

  • To propose a novel quasi-likelihood method for estimating GLMs with limited dependent variables.
  • To address the unresolved issue of quasi-likelihood estimation in these models.
  • To develop a unified estimation approach for limited dependent variable models.

Main Methods:

  • Introduction of Taylor quasi-likelihood based on Taylor expansion of distribution or likelihood functions.
  • Extension of the likelihood to generalized and adaptive versions.
  • Proposal of a distributed procedure for likelihood estimator computation.

Main Results:

  • Development of selection criteria for the proposed method in low-dimensional settings.
  • Theoretical arguments for the consistency and asymptotic normality of the estimator.
  • Discussion of feature selection and oracle properties in high-dimensional settings.

Conclusions:

  • The proposed Taylor quasi-likelihood method effectively handles unified estimation for limited dependent variable models.
  • The method demonstrates advantages in both low- and high-dimensional scenarios.
  • Simulation results validate the efficacy and benefits of the novel approach.