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Locally kernel weighted maximum likelihood estimator for local linear multi-predictor poisson regression.

Darnah1, Memi Nor Hayati1, Sri Wahyuningsih1

  • 1Department of Mathematics, Faculty of Mathematics and Natural Sciences, Mulawarman University, Indonesia.

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Summary
This summary is machine-generated.

This study introduces a novel local linear multi-predictor Poisson regression model. It optimizes bandwidth selection using maximum likelihood cross-validation (MLCV) and applies it to health data, specifically childhood stunting in East Kalimantan.

Keywords:
KernelLocal linearLocally Kernel Weighted Maximum Likelihood Estimator for Local Linear Multi-predictor Poisson RegressionMLCVNewton-RaphsonPoisson regressionStunting

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Area of Science:

  • Statistics
  • Biostatistics
  • Econometrics

Background:

  • Poisson regression models are widely used for count data analysis.
  • Existing models may not adequately capture complex relationships in multi-predictor scenarios.
  • Local regression approaches offer flexibility in modeling non-linear patterns.

Purpose of the Study:

  • To introduce a new local linear multi-predictor Poisson regression model.
  • To establish an optimal bandwidth selection method using maximum likelihood cross-validation (MLCV).
  • To apply the developed model to analyze health data, focusing on childhood stunting.

Main Methods:

  • Development of a local linear multi-predictor Poisson regression model.
  • Utilization of maximum likelihood cross-validation (MLCV) for optimal bandwidth selection.
  • Application of kernel-weighted maximum likelihood estimation and Newton-Raphson iteration for parameter estimation.

Main Results:

  • A novel regression model was successfully developed for multi-predictor Poisson data.
  • The MLCV method provided an effective approach for optimal bandwidth selection.
  • The model was successfully applied to analyze the stunting case in East Kalimantan, demonstrating its utility in health data analysis.

Conclusions:

  • The proposed local linear multi-predictor Poisson regression model offers a flexible and effective approach for analyzing complex count data.
  • MLCV is a reliable method for determining optimal bandwidth in local regression.
  • The model's application to stunting data highlights its potential for public health research and policy.